minimax game.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Minimax Game\n",
    "\n",
    "There is a vehicle with many vulnerabilities in it.  \n",
    "Each vulnerability has:\n",
    "- a cost to attack\n",
    "- a cost to defend\n",
    "- a probability of successfully attacking\n",
    "- a probability of successfully defending\n",
    "- a severity if an attack is successful\n",
    "\n",
    "Two players\n",
    "- defender\n",
    "- attacker\n",
    "\n",
    "It's a simultaneous-play one-shot game; each player picks an action at the same then the game is over.\n",
    "\n",
    "The actions in this game are simply selection of vulnerabilities to attack or defend.\n",
    "The players have a budget which constrains the actions they can take."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# lets try and stay type-safe :P\n",
    "from typing import *\n",
    "import random\n",
    "from dataclasses import dataclass, field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass(frozen=True)\n",
    "class Vulnerability: # this could probably be a dataclass\n",
    "    id: int\n",
    "    attackerCost: int = field(default_factory=lambda: random.randint(1,5))\n",
    "    defenderCost: int = field(default_factory=lambda: random.randint(1,5))\n",
    "    attackerProb: float = field(default_factory=lambda: round(random.uniform(0.05,0.98),2))\n",
    "    defenderProb: float = field(default_factory=lambda: round(random.uniform(0.05,0.98),2))\n",
    "    severity: int = field(default_factory=lambda: random.randint(1,5))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Vulnerability(id=123, attackerCost=4, defenderCost=5, attackerProb=0.82, defenderProb=0.25, severity=5)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vulnerability(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass(frozen=True)\n",
    "class Vehicle:\n",
    "    vulns: List[Vulnerability] = field(default_factory=list)\n",
    "    \n",
    "    @staticmethod\n",
    "    def get_random_vehicle(num_vulns: int) -> Vehicle:\n",
    "        return Vehicle(vulns=[Vulnerability(x) for x in range(num_vulns)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Vehicle(vulns=[Vulnerability(id=0, attackerCost=3, defenderCost=2, attackerProb=0.87, defenderProb=0.74, severity=5), Vulnerability(id=1, attackerCost=2, defenderCost=1, attackerProb=0.43, defenderProb=0.25, severity=5), Vulnerability(id=2, attackerCost=1, defenderCost=2, attackerProb=0.46, defenderProb=0.65, severity=5), Vulnerability(id=3, attackerCost=1, defenderCost=4, attackerProb=0.31, defenderProb=0.09, severity=5)])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vehicle.get_random_vehicle(4)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "helper function for powerset; gets all subsets of a list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = TypeVar(\"T\")\n",
    "def powerset(s: List[T]) -> List[List[T]]:\n",
    "    import itertools\n",
    "    return itertools.chain.from_iterable(itertools.combinations(s, r) for r in range(1, len(s)+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0,),\n",
       " (1,),\n",
       " (2,),\n",
       " (3,),\n",
       " (0, 1),\n",
       " (0, 2),\n",
       " (0, 3),\n",
       " (1, 2),\n",
       " (1, 3),\n",
       " (2, 3),\n",
       " (0, 1, 2),\n",
       " (0, 1, 3),\n",
       " (0, 2, 3),\n",
       " (1, 2, 3),\n",
       " (0, 1, 2, 3)]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(powerset(range(4)))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utility is calculated according to \n",
    "\n",
    "$$\n",
    "\n",
    "                    \\begin{equation}\n",
    "                        U^a(a^a, a^d) := \n",
    "                        \\sum_{v_k \\in a^a}\n",
    "                        \\begin{cases}\n",
    "                        (1-p^d_k)*p^a_k*s_k^2 & v_k \\in a^d \\\\\n",
    "                        p^a_k*s_k^2 & v_k \\notin a^d \\\\\n",
    "                        \\end{cases}\n",
    "                    \\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_attacker_utility(\n",
    "    defending: List[Vulnerability],\n",
    "    attacking: List[Vulnerability]\n",
    ") -> float:\n",
    "    defendingLookup = set([x.id for x in defending])\n",
    "    rtn = 0\n",
    "    for v in attacking:\n",
    "        if v.id in defendingLookup:\n",
    "            rtn += (v.severity ** 2) * v.attackerProb * (1-v.defenderProb)\n",
    "        else:\n",
    "            rtn += (v.severity ** 2) * v.attackerProb\n",
    "    return rtn"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solution container class, calculates the probability of a compromise occurring for each severity 1-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SubgameSolution:\n",
    "    defender_util: int\n",
    "    severity_chances: List[float]\n",
    "    dchoice: List[Vehicle]\n",
    "    achoice: List[Vehicle]\n",
    "    def __init__(self, dchoice: List[Vulnerability], achoice: List[Vulnerability]) -> None:\n",
    "        self.dchoice = dchoice\n",
    "        self.achoice = achoice\n",
    "        self.defender_util = round(-get_attacker_utility(dchoice, achoice),2)\n",
    "        # Start off as the chance that it is not compromised\n",
    "        self.severity_chances = {\n",
    "            1:1,\n",
    "            2:1,\n",
    "            3:1,\n",
    "            4:1,\n",
    "            5:1\n",
    "        }\n",
    "        defendingLookup = set([x.id for x in dchoice])\n",
    "        for vuln in achoice:\n",
    "            # Decrease the chance it is not compromised by the chance the attacks fail\n",
    "            if vuln.id in defendingLookup:\n",
    "                self.severity_chances[vuln.severity] *= 1-(vuln.attackerProb * (1-vuln.defenderProb))\n",
    "            else:\n",
    "                self.severity_chances[vuln.severity] *= 1-(vuln.attackerProb)\n",
    "\n",
    "        # Convert to the chance that a compromise with the given severity is _successful_\n",
    "        for k in self.severity_chances.keys():\n",
    "            self.severity_chances[k] = round(1 - self.severity_chances[k],2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solver function, takes a game and returns the optimal solution.\n",
    "\n",
    "Expected attacker utility: \n",
    "$$\n",
    "\n",
    "                    \\begin{equation}\n",
    "                        U^a_{expected} := \\max_{a^a \\in \\mathcal{A}^a} \\min_{a^d \\in \\mathcal{A}^d} U^a(a^a, a^d)\n",
    "                    \\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_optimal_actions(\n",
    "    vehicle: Vehicle,\n",
    "    attacker_budget: int,\n",
    "    defender_budget: int,\n",
    ") -> SubgameSolution:\n",
    "    action_space = list(powerset(vehicle.vulns))\n",
    "\n",
    "    # track best possible defender action seen so far\n",
    "    best_defender_util = -1e100\n",
    "    best_defender_subset = None\n",
    "    best_attacker_subset = None\n",
    "\n",
    "    # For each possible defender action\n",
    "    for dchoice in action_space:\n",
    "        # If the defender's budget is exceeded, action isn't legal\n",
    "        if sum([x.defenderCost for x in dchoice]) > defender_budget: continue\n",
    "\n",
    "        # track best possible attacker response seen so far\n",
    "        temp_best_attacker_util = 0\n",
    "        temp_best_attacker_subset = None\n",
    "        # For each possible attacker action\n",
    "        for achoice in action_space:\n",
    "            # If the attacker's budget is exceeded, action isn't legal\n",
    "            if sum([x.attackerCost for x in achoice]) > attacker_budget: continue\n",
    "\n",
    "            # get the utility for the chosen actions\n",
    "            attacker_util = get_attacker_utility(dchoice, achoice)\n",
    "            # if it's better for the attacker, update the best attacker response\n",
    "            if attacker_util > temp_best_attacker_util:\n",
    "                temp_best_attacker_util = attacker_util\n",
    "                temp_best_attacker_subset = achoice\n",
    "\n",
    "        # Defender utility is negative of attacker util; zero-sum game\n",
    "        defender_util = -1 * temp_best_attacker_util\n",
    "        # if it's better for the defender, update the best defender action\n",
    "        if defender_util > best_defender_util:\n",
    "            best_defender_util = defender_util\n",
    "            best_defender_subset = dchoice\n",
    "            best_attacker_subset = temp_best_attacker_subset\n",
    "    return SubgameSolution(best_defender_subset, best_attacker_subset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "vehicle = Vehicle.get_random_vehicle(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Vulnerability(id=0, attackerCost=5, defenderCost=3, attackerProb=0.2, defenderProb=0.19, severity=3),\n",
       " Vulnerability(id=1, attackerCost=4, defenderCost=5, attackerProb=0.32, defenderProb=0.08, severity=5),\n",
       " Vulnerability(id=2, attackerCost=2, defenderCost=1, attackerProb=0.82, defenderProb=0.64, severity=3),\n",
       " Vulnerability(id=3, attackerCost=2, defenderCost=3, attackerProb=0.55, defenderProb=0.16, severity=1),\n",
       " Vulnerability(id=4, attackerCost=1, defenderCost=4, attackerProb=0.96, defenderProb=0.39, severity=4),\n",
       " Vulnerability(id=5, attackerCost=1, defenderCost=4, attackerProb=0.47, defenderProb=0.74, severity=4),\n",
       " Vulnerability(id=6, attackerCost=3, defenderCost=4, attackerProb=0.33, defenderProb=0.81, severity=2),\n",
       " Vulnerability(id=7, attackerCost=1, defenderCost=5, attackerProb=0.38, defenderProb=0.34, severity=2)]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vehicle.vulns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21.4068"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "action_space = list(powerset(vehicle.vulns))\n",
    "# preview utility for some arbitrary actions\n",
    "get_attacker_utility(action_space[15], action_space[222])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "defender utility: -23.5\n",
      "compromise probability for each severity: {1: 0, 2: 0.38, 3: 0.3, 4: 0.64, 5: 0.32}\n",
      "\n",
      "Vulnerabilities and actions taken:\n",
      "Vulnerability(id=0, attackerCost=5, defenderCost=3, attackerProb=0.2, defenderProb=0.19, severity=3)\t\t\n",
      "Vulnerability(id=1, attackerCost=4, defenderCost=5, attackerProb=0.32, defenderProb=0.08, severity=5)\t\tA\n",
      "Vulnerability(id=2, attackerCost=2, defenderCost=1, attackerProb=0.82, defenderProb=0.64, severity=3)\tD\tA\n",
      "Vulnerability(id=3, attackerCost=2, defenderCost=3, attackerProb=0.55, defenderProb=0.16, severity=1)\t\t\n",
      "Vulnerability(id=4, attackerCost=1, defenderCost=4, attackerProb=0.96, defenderProb=0.39, severity=4)\tD\tA\n",
      "Vulnerability(id=5, attackerCost=1, defenderCost=4, attackerProb=0.47, defenderProb=0.74, severity=4)\tD\tA\n",
      "Vulnerability(id=6, attackerCost=3, defenderCost=4, attackerProb=0.33, defenderProb=0.81, severity=2)\t\t\n",
      "Vulnerability(id=7, attackerCost=1, defenderCost=5, attackerProb=0.38, defenderProb=0.34, severity=2)\t\tA\n"
     ]
    }
   ],
   "source": [
    "solution = get_optimal_actions(vehicle, attacker_budget=10, defender_budget=10)\n",
    "print(\"defender utility:\", solution.defender_util)\n",
    "print(\"compromise probability for each severity:\", solution.severity_chances)\n",
    "print(\"\\nVulnerabilities and actions taken:\")\n",
    "for v in vehicle.vulns:\n",
    "    print(v, end=\"\\t\")\n",
    "    if v in solution.dchoice:\n",
    "        print(\"D\", end=\"\\t\")\n",
    "    else:\n",
    "        print(\"\\t\", end=\"\")\n",
    "    if v in solution.achoice:\n",
    "        print(\"A\", end=\"\")\n",
    "    print()"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Format as a LaTeX table, should look something like this when rendered (tho the numbers will be different):\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\\begin{table}\n",
      "    \\centering\n",
      "    \\begin{tabular}{|p{8mm}|p{8mm}|p{8mm}|p{8mm}|p{8mm}|p{8mm}|p{4mm}|p{4mm}|}\n",
      "        \\hline\n",
      "        $i$ & $p^a_i$ & $p^d_i$ & $c^a_i$ & $c^d_i$ & $s_i$ & $*^a$ & $*^d$ \\\\\n",
      "        \\hline\n",
      "        1 & 0.96 & 0.58 & 4 & 5 & 5 & \\cellcolor{red!50} & \\cellcolor{blue!50}\\\\\n",
      "\t\\hline\n",
      "\t2 & 0.71 & 0.84 & 2 & 1 & 5 & & \\cellcolor{blue!50}\\\\\n",
      "\t\\hline\n",
      "\t3 & 0.78 & 0.82 & 4 & 3 & 1 & & \\\\\n",
      "\t\\hline\n",
      "\t4 & 0.81 & 0.46 & 4 & 1 & 4 & & \\cellcolor{blue!50}\\\\\n",
      "\t\\hline\n",
      "\t5 & 0.2 & 0.24 & 5 & 2 & 2 & & \\\\\n",
      "\t\\hline\n",
      "\t6 & 0.82 & 0.81 & 1 & 3 & 1 & & \\\\\n",
      "\t\\hline\n",
      "\t7 & 0.82 & 0.53 & 5 & 3 & 5 & \\cellcolor{red!50} & \\cellcolor{blue!50}\\\\\n",
      "\t\\hline\n",
      "\t8 & 0.42 & 0.81 & 1 & 3 & 4 & \\cellcolor{red!50} & \\\\\n",
      "\t\\hline\n",
      "    \\end{tabular}\n",
      "    \\caption{Example set of vulnerabilities in the minimax game with parameters $\\zeta^a=\\zeta^d=10$, $n$=8. The coloured cells represent inclusion in the optimal strategy, with red representing the attacker's optimal strategy and blue representing the defender's optimal strategy.}\n",
      "    \\label{tab:vulnexample}\n",
      "\\end{table}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# format for LaTeX table\n",
    "# this will render properly with used in a full LaTeX document, the but lightweight stuff used with Jupyter doesn't like it :(\n",
    "template = r\"\"\"\n",
    "\\begin{table}\n",
    "    \\centering\n",
    "    \\begin{tabular}{|p{8mm}|p{8mm}|p{8mm}|p{8mm}|p{8mm}|p{8mm}|p{4mm}|p{4mm}|}\n",
    "        \\hline\n",
    "        $i$ & $p^a_i$ & $p^d_i$ & $c^a_i$ & $c^d_i$ & $s_i$ & $*^a$ & $*^d$ \\\\\n",
    "        \\hline\n",
    "        %BODY%\n",
    "    \\end{tabular}\n",
    "    \\caption{Example set of vulnerabilities in the minimax game with parameters $\\zeta^a=\\zeta^d=10$, $n$=8. The coloured cells represent inclusion in the optimal strategy, with red representing the attacker's optimal strategy and blue representing the defender's optimal strategy.}\n",
    "    \\label{tab:vulnexample}\n",
    "\\end{table}\n",
    "\"\"\"\n",
    "body = \"\"\n",
    "for v in vehicle.vulns:\n",
    "    body += f\"{v.id+1} & {v.attackerProb} & {v.defenderProb} & {v.attackerCost} & {v.defenderCost} & {v.severity} & \"\n",
    "    if v in solution.achoice:\n",
    "        body += r\"\\cellcolor{red!50} & \"\n",
    "    else:\n",
    "        body += \"& \"\n",
    "    if v in solution.dchoice:\n",
    "        body += r\"\\cellcolor{blue!50}\"\n",
    "    body += \"\\\\\\\\\\n\\t\\\\hline\\n\\t\"\n",
    "table = template.replace(\"%BODY%\", body.rstrip())\n",
    "print(table)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lets explore the solution space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "solutions: List[SubgameSolution] = []"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sample 1000 random games and find the solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8839b8e2c4df404fbaee869bee40a567",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tqdm.notebook import tqdm\n",
    "from IPython.display import clear_output\n",
    "\n",
    "for i in tqdm(range(1000 - len(solutions))): # idempotent\n",
    "    s = get_optimal_actions(Vehicle.get_random_vehicle(8), 10, 10)\n",
    "    solutions.append(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best and worst games for the defender\n",
      "defender util=-2.51 {1: 0.92, 2: 0.25, 3: 0, 4: 0, 5: 0}\n",
      "defender util=-61.21 {1: 0, 2: 0, 3: 0, 4: 0.43, 5: 0.98}\n"
     ]
    }
   ],
   "source": [
    "solutions = sorted(solutions, key=lambda x: x.defender_util, reverse=True)\n",
    "print(\"The best and worst games for the defender\")\n",
    "for s in [solutions[0], solutions[-1]]:\n",
    "    print(f\"defender util={s.defender_util}\", s.severity_chances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams.update({\"figure.figsize\":(7,5), \"figure.dpi\":100})\n",
    "\n",
    "bins = np.linspace(0,1,10)\n",
    "\n",
    "plt.hist([[s.severity_chances[i] for s in solutions] for i in range(1,6)], bins, alpha=0.2, label=[f\"Severity {i}\" for i in range(1,6)])\n",
    "# plt.hist(human, bins, alpha=0.5, label=\"human\")\n",
    "# plt.hist(ai, bins, alpha=0.5, label=\"ai\")\n",
    "plt.xticks(np.arange(0,1,0.1))\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.title(f\"Sampled probabilities of successful attack\")\n",
    "plt.xlabel(\"Probability\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.show()\n",
    "# plt.gca().set(title=\"Freq histogram\", ylabel=\"Freq\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist([s.defender_util for s in solutions], bins=50)\n",
    "plt.title(\"Sampled optimal defender utilities\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write to JSON for use in other stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "with open(\"minimax-game-solutions.json\",\"w\") as f:\n",
    "    json.dump(solutions, f, default=vars, indent=4)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.12 ('subgame')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.15"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "09b31e4957d63d79e1e76c5537c345194b9f565583fac53cbbb105281d72baf4"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}