HW1_DIA3_ThomasDANIEL.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overall solution description. Work done by Thomas DANIEL  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:red\">My EightPuzzle class and the search algorithms are highely inspired by the code found in the differents notebooks and LABS in the AI algorithm course \n",
    "from Farah AIT SALAHT.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PROBLEM FORMULATION: \n",
    "\n",
    "Question A. All others questions are either discussed within the code or answered at the end of the notebook\n",
    "\n",
    "We are given a 3x3 grid with numbers ranging from 1 to 8 with one blank space. Each tiles can switch place with the blank space. The blank space as at most 4 possibilities : up,down,right,left. \n",
    "\n",
    "States: The different disposition of the grid.\n",
    "\n",
    "Possibles actions: movements available for the blank space (up,down,right,left depending on the position)\n",
    "\n",
    "Initial state: grid state at the beginning\n",
    "\n",
    "Goal State: grid ordered correctly as follows : [[0,1,2],[3,4,5],[6,7,8]]. Here the blank is replaced by a 0. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Important librairies: \n",
    "\n",
    "-heapq\n",
    "\n",
    "-time\n",
    "\n",
    "-random\n",
    "\n",
    "-statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'this module will be useful for the benchmarks'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import heapq\n",
    "\"\"\" Heapq will allow us to build our search algorithms. It provides priority queues which are widely used in search algorithm to find the next node to \n",
    "explore based on the total cost (f+g in the case of A*)\"\"\"\n",
    "\n",
    "import time\n",
    "\"\"\"The time library will allow us to get the compute time of our algorithms to make benchmarks and compare them.\"\"\"\n",
    "\n",
    "import random\n",
    "\n",
    "\"\"\"The random module will help us build random initial states to conduct benchmarks.\"\"\"\n",
    "\n",
    "from statistics import mean\n",
    "\n",
    "\"\"\"this module will be useful for the benchmarks\"\"\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "EigthPuzzle Class : Here is the code of my EightPuzzle Class. I will go through the designs choice steps just after. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class EightPuzzle:\n",
    "\n",
    "    def __init__(self, initial_state, goal_state):\n",
    "        \"\"\"Class constructor. We take as arguments the initial state and goal state.\n",
    "        I choose to convert the 3x3 matrix into a tuple to be able to use sets in my search algorithms implementation. \n",
    "        I also choose to store the size of the grid to make it easier for some function implementations. \n",
    "        \"\"\"\n",
    "        self.initial_state = tuple(map(tuple, initial_state)) #Convert the 3x3 matrix list into a tuple\n",
    "        self.goal_state = tuple(map(tuple, goal_state))#Convert the 3x3 matrix list into a tuple\n",
    "        self.size = 3 #size of the matrix\n",
    "\n",
    "    def get_blank_position(self, state):\n",
    "        \"\"\"Function to get the blank position in the grid that is represented by a 0.\n",
    "           I choose to build the function to be able to get the position rapidly. \n",
    "        \"\"\"\n",
    "        for i in range(self.size):\n",
    "            for j in range(self.size):\n",
    "                if state[i][j] == 0: \n",
    "                    return i, j\n",
    "\n",
    "    def get_neighbors(self, state):\n",
    "        \"\"\"Generate all possible neighboring states by moving the blank tile in one of the four possible directions\n",
    "        (up, down, left, right), ensuring moves stay within bounds of the puzzle.\"\"\"\n",
    "\n",
    "        i, j = self.get_blank_position(state)  # Get the blank tile's position\n",
    "        neighbors = []\n",
    "        # Define possible moves for the blank tile: (row offset, column offset)\n",
    "        for di, dj in [(-1, 0), (1, 0), (0, -1), (0, 1)]:  # Up, down, left, right\n",
    "            new_i, new_j = i + di, j + dj\n",
    "            if 0 <= new_i < self.size and 0 <= new_j < self.size:  # Ensure the new position is within bounds\n",
    "                new_state = [list(row) for row in state]  # Create a copy of the current state as a list of lists\n",
    "                # Swap the blank tile with the neighboring tile\n",
    "                new_state[i][j], new_state[new_i][new_j] = new_state[new_i][new_j], new_state[i][j]\n",
    "                neighbors.append(tuple(map(tuple, new_state)))  # Convert to tuple and add to neighbors\n",
    "        return neighbors\n",
    "\n",
    "    def is_goal(self, state):\n",
    "        \"\"\"Check if the current state matches the goal state.\n",
    "        This function is used to determine if a solution has been found.\"\"\"\n",
    "        return state == self.goal_state\n",
    "\n",
    "    def h1_misplaced_tiles(self, state):\n",
    "        \"\"\"Heuristic 1: Misplaced tiles. First heuristic implementation asked in the subject.\n",
    "        We just check if the tile is different from the tile goal state and from 0. \"\"\"\n",
    "        return sum(1 for i in range(self.size) for j in range(self.size) if state[i][j] != self.goal_state[i][j] and state[i][j] != 0)\n",
    "\n",
    "    def h2_manhattan_distance(self, state):\n",
    "        \"\"\"Heuristic 2: Manhattan distance. This heuristic calculates the sum of the Manhattan distances between each tile's current position\n",
    "        and its goal position. Manhattan distance is the total number of vertical and horizontal moves\n",
    "        needed to reach the goal position.\"\"\"\n",
    "        distance = 0\n",
    "        goal = self.goal_state\n",
    "        for i in range(self.size):\n",
    "            for j in range(self.size):\n",
    "                # Skip the blank tile\n",
    "                if state[i][j] == 0:\n",
    "                    continue\n",
    "                # Find the current tile's value\n",
    "                tile_value = state[i][j]\n",
    "                # Find the target position of the tile in the goal state\n",
    "                target_position = [(index, row.index(tile_value)) for index, row in enumerate(goal) if tile_value in row]\n",
    "                # Since tile_value will be unique in a valid puzzle, we can safely get the first match\n",
    "                if target_position:\n",
    "                    target_row, target_col = target_position[0]  \n",
    "                    # Calculate Manhattan distance\n",
    "                    distance += abs(i - target_row) + abs(j - target_col)\n",
    "        return distance\n",
    "    \n",
    "    def h3_row_column_mismatch(self, state):\n",
    "        \"\"\"Heuristic 3: Number of tiles not in the correct row + number of tiles not in the correct column\"\"\"\n",
    "        row_mismatch = 0\n",
    "        column_mismatch = 0\n",
    "        goal = self.goal_state\n",
    "\n",
    "        for i in range(self.size):\n",
    "            for j in range(self.size):\n",
    "                # Find the current tile's value\n",
    "                tile_value = state[i][j]\n",
    "                # Find the target position of the tile in the goal state\n",
    "                target_position = [(index, row.index(tile_value)) for index, row in enumerate(goal) if tile_value in row]\n",
    "                if target_position:\n",
    "                    goal_i, goal_j = target_position[0]\n",
    "                    # Check if the tile is in the correct row\n",
    "                    if i != goal_i:\n",
    "                        row_mismatch += 1\n",
    "                    # Check if the tile is in the correct column\n",
    "                    if j != goal_j:\n",
    "                        column_mismatch += 1\n",
    "\n",
    "        return row_mismatch + column_mismatch  # Return the total number of mismatches\n",
    "\n",
    "    \n",
    "    def h4_linear_conflict(self, state):\n",
    "        \"\"\"Heuristic 4: Linear Conflict. This heuristic adds penalties for pairs of tiles that are in the correct row or column \n",
    "        but in the wrong order, in addition to their Manhattan distances. Each conflicting pair contributes an additional 2 moves.\"\"\"\n",
    "        \n",
    "        manhattan_distance = self.h2_manhattan_distance(state)\n",
    "        linear_conflict = 0\n",
    "\n",
    "        # Check for row conflicts\n",
    "        for i in range(self.size):\n",
    "            goal_positions = [divmod(state[i][j] - 1, self.size)[1] for j in range(self.size) if state[i][j] != 0 and divmod(state[i][j] - 1, self.size)[0] == i]\n",
    "            for j in range(len(goal_positions)):\n",
    "                for k in range(j + 1, len(goal_positions)):\n",
    "                    if goal_positions[j] > goal_positions[k]:  # Conflict detected\n",
    "                        linear_conflict += 2\n",
    "\n",
    "        # Check for column conflicts\n",
    "        for j in range(self.size):\n",
    "            goal_positions = [divmod(state[i][j] - 1, self.size)[0] for i in range(self.size) if state[i][j] != 0 and divmod(state[i][j] - 1, self.size)[1] == j]\n",
    "            for i in range(len(goal_positions)):\n",
    "                for k in range(i + 1, len(goal_positions)):\n",
    "                    if goal_positions[i] > goal_positions[k]:  # Conflict detected\n",
    "                        linear_conflict += 2\n",
    "\n",
    "        return manhattan_distance + linear_conflict\n",
    "\n",
    "    def uniform_cost_search(self):\n",
    "        \"\"\"Uniform Cost Search (UCS) with node expansion tracking. UCS is a search algorithm that expands the node with the lowest cost first.\n",
    "        It treats every move with a uniform cost (1 in this case) and is guaranteed to find the optimal solution.\"\"\"\n",
    "        start_node = (self.initial_state, [], 0)  # (state, path, cost): initial state, empty path, and zero cost\n",
    "        frontier = [(0, start_node)]  # Priority queue (min-heap) where elements are prioritized by cost\n",
    "        explored = set()  # Set to track explored states\n",
    "        expanded_order = []  # List to track the order of node expansions\n",
    "\n",
    "        while frontier:\n",
    "            _, (state, path, cost) = heapq.heappop(frontier)  # Get the node with the lowest cost\n",
    "            expanded_order.append(state)  # Record the expansion of this node\n",
    "\n",
    "            if self.is_goal(state):  # If goal is reached, return the solution path and expansion order\n",
    "                return path, expanded_order\n",
    "\n",
    "            if state not in explored:  # Only expand the node if it hasn't been explored yet\n",
    "                explored.add(state)\n",
    "\n",
    "                # Expand all neighbors of the current state\n",
    "                for neighbor in self.get_neighbors(state):\n",
    "                    if neighbor not in explored:\n",
    "                        new_path = path + [neighbor]  # Update path with the neighbor\n",
    "                        new_cost = cost + 1  # Each move has a uniform cost of 1\n",
    "                        new_node = (neighbor, new_path, new_cost)\n",
    "                        heapq.heappush(frontier, (new_cost, new_node))  # Add neighbor to frontier with new cost\n",
    "\n",
    "        return None, expanded_order  # Return failure if no solution is found\n",
    "\n",
    "    \n",
    "    def best_first_search(self, heuristic):\n",
    "        \"\"\"Best-First Search using the given heuristic. Best-First Search prioritizes nodes based on the heuristic function, \n",
    "        without considering the path cost. It is not guaranteed to find the optimal solution unless used with an admissible \n",
    "        heuristic like Manhattan distance.\"\"\"   \n",
    "        frontier = [(heuristic(self.initial_state), [self.initial_state])]  # Priority queue prioritized by heuristic value\n",
    "        visited = set([self.initial_state])  # Set to track visited states\n",
    "        expanded_nodes = 0  # Count of expanded nodes\n",
    "\n",
    "        while frontier:\n",
    "            _, path = heapq.heappop(frontier)  # Get the node with the lowest heuristic value\n",
    "            expanded_nodes += 1  # Increment the count of expanded nodes\n",
    "            current_state = path[-1]  # The current state is the last one in the path\n",
    "\n",
    "            if self.is_goal(current_state):  # If goal is reached, return the solution path and number of expanded nodes\n",
    "                return path, expanded_nodes\n",
    "\n",
    "            # Expand neighbors of the current state\n",
    "            for neighbor in self.get_neighbors(current_state):\n",
    "                if neighbor not in visited:\n",
    "                    visited.add(neighbor)\n",
    "                    new_path = path + [neighbor]  # Update the path\n",
    "                    heapq.heappush(frontier, (heuristic(neighbor), new_path))  # Push neighbor with heuristic value\n",
    "\n",
    "        return None, expanded_nodes  # Return failure if no solution is found\n",
    "\n",
    "    def a_star_search(self, heuristic):\n",
    "        \"\"\"A* Search using the given heuristic. A* Search combines the cost of the path so far (g) with the heuristic (h) to guide the search.\n",
    "        It is guaranteed to find the optimal solution if the heuristic is admissible (e.g., Manhattan distance).\"\"\"\n",
    "        \n",
    "        start_node = (0, [self.initial_state])  # (g, path), where g is the cost and path is the list of states\n",
    "        start_f = heuristic(self.initial_state)  # f = g + h, where g = 0 initially\n",
    "        frontier = [(start_f, start_node)]  # Priority queue (min-heap) based on f = g + h\n",
    "        visited = set([self.initial_state])  # Set to track visited states\n",
    "        expanded_nodes = 0  # Count of expanded nodes\n",
    "\n",
    "        while frontier:\n",
    "            # Get the node with the lowest f = g + h\n",
    "            _, (g, path) = heapq.heappop(frontier)\n",
    "            expanded_nodes += 1\n",
    "            current_state = path[-1]  # Get the last state in the path\n",
    "\n",
    "            # If goal is reached, return the solution path and number of expanded nodes\n",
    "            if self.is_goal(current_state):\n",
    "                return path, expanded_nodes\n",
    "\n",
    "            # Expand neighbors of the current state\n",
    "            for neighbor in self.get_neighbors(current_state):\n",
    "                if neighbor not in visited:\n",
    "                    visited.add(neighbor)\n",
    "                    new_g = g + 1  # Each move has a cost of 1\n",
    "                    new_f = new_g + heuristic(neighbor)  # f = g + h\n",
    "                    new_path = path + [neighbor]\n",
    "                    heapq.heappush(frontier, (new_f, (new_g, new_path)))\n",
    "\n",
    "        return None, expanded_nodes  # Return failure if no solution is found"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implementation choices: \n",
    "\n",
    "-I choose to convert the matrix into a tuple to be able to use a set() to store explored nodes. The set() is a better data collection than a list. \n",
    "\n",
    "-Blank function to get the position of the blank space in the matrix (tuple), very useful in the neighbor function. \n",
    "\n",
    "-Neighbor function: quite a mandatory function as it is used to find where to expand next in the search functions....\n",
    "\n",
    "-We could have coded the best first search and UCS in the same function and just change the heuristic ( 0 or 1 depends on the algorithm) but i choose to\n",
    "code separated functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionnal functions outside of the class: \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I also choose to add a function to check if the initial state of the puzzle is solvable. In case the user wants to give his own initial state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_solvable(puzzle):\n",
    "  \"\"\"Check if an 8-puzzle is solvable.\"\"\"\n",
    "  # Flatten the puzzle into a single list\n",
    "  flat_puzzle = [tile for row in puzzle for tile in row]\n",
    "  \n",
    "  # Count the number of inversions\n",
    "  inversions = 0\n",
    "  for i in range(len(flat_puzzle)):\n",
    "    for j in range(i + 1, len(flat_puzzle)):\n",
    "      if flat_puzzle[i] != 0 and flat_puzzle[j] != 0 and flat_puzzle[i] > flat_puzzle[j]:\n",
    "        inversions += 1\n",
    "  \n",
    "  # The puzzle is solvable if the number of inversions is even\n",
    "  return inversions % 2 == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generating a random initial state to be able to conduct benchmarks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to generate a random solvable 8-puzzle\n",
    "def generate_random_puzzle(goal_state):\n",
    "    while True:\n",
    "        # Flatten the goal state into a single list of tiles\n",
    "        puzzle = [tile for row in goal_state for tile in row]\n",
    "        # Shuffle the tiles randomly\n",
    "        random.shuffle(puzzle)\n",
    "        # Convert the shuffled list back into a 3x3 grid\n",
    "        random_puzzle = [puzzle[i:i + 3] for i in range(0, len(puzzle), 3)]\n",
    "        # Check if the generated puzzle is solvable\n",
    "        if is_solvable(random_puzzle):\n",
    "            return random_puzzle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Benchmark Time !\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I first build a function run_benchmark that does the following: \n",
    "\n",
    "For each search algorithm it will get : time to run the search, number of nodes expanded, final path solution (complete path to goal state).\n",
    "\n",
    "To answer the question from the homework I only displayed all the expanded nodes of UCS (as it is not asked for other searches)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_benchmark(initial_state, goal_state):\n",
    "    puzzle = EightPuzzle(initial_state, goal_state) #instantiate an EightPuzzle object\n",
    "\n",
    "    # Uniform Cost Search (UCS) Specific code as it is asked to display all expanded nodes. \n",
    "    print(\"Running Uniform Cost Search (UCS)...\")\n",
    "    start_time = time.time()\n",
    "    solution_ucs, expanded_ucs_order = puzzle.uniform_cost_search()\n",
    "    time_ucs = time.time() - start_time\n",
    "    path_length_ucs=len(solution_ucs)\n",
    "    # Display UCS results\n",
    "    print(\"\\nUCS - Order of Expanded Nodes:\")\n",
    "    for i, node in enumerate(expanded_ucs_order):\n",
    "        print(f\"Step {i + 1}:\")\n",
    "        for row in node:\n",
    "            print(row)\n",
    "        print()\n",
    "    #Display Solution Path\n",
    "    print(\"UCS - Solution Path:\")\n",
    "    for i, node in enumerate(solution_ucs):\n",
    "        print(f\"Step {i + 1}:\")\n",
    "        for row in node:\n",
    "            print(row)\n",
    "        print()\n",
    "\n",
    "    print(f\"UCS - Path length: {len(solution_ucs)}\")\n",
    "    print(f\"UCS - Time taken: {time_ucs:.4f} seconds\")\n",
    "    \n",
    "\n",
    "    # Best-First Search with h1 (misplaced tiles)\n",
    "    print(\"Running Best-First Search (h1: Misplaced Tiles)...\")\n",
    "    start_time = time.time()\n",
    "    solution_bfs_h1, expanded_bfs_h1 = puzzle.best_first_search(puzzle.h1_misplaced_tiles)\n",
    "    time_bfs_h1 = time.time() - start_time\n",
    "    path_length_bfs_h1 = len(solution_bfs_h1)\n",
    "\n",
    "    # Best-First Search with h2 (Manhattan distance)\n",
    "    print(\"Running Best-First Search (h2: Manhattan Distance)...\")\n",
    "    start_time = time.time()\n",
    "    solution_bfs_h2, expanded_bfs_h2 = puzzle.best_first_search(puzzle.h2_manhattan_distance)\n",
    "    time_bfs_h2 = time.time() - start_time\n",
    "    path_length_bfs_h2 = len(solution_bfs_h2)\n",
    "\n",
    "    # Best-First Search with h3 (nb_tiles row +col)\n",
    "    print(\"Running Best-First Search (h3: nb_tiles row + col)...\")\n",
    "    start_time = time.time()\n",
    "    solution_bfs_h3, expanded_bfs_h3 = puzzle.best_first_search(puzzle.h3_row_column_mismatch)\n",
    "    time_bfs_h3 = time.time() - start_time\n",
    "    path_length_bfs_h3= len(solution_bfs_h3)\n",
    "\n",
    "    # Best-First Search with h3 (nb_tiles row +col)\n",
    "    print(\"Running Best-First Search (h4 : Manhattan + linear conflict)...\")\n",
    "    start_time = time.time()\n",
    "    solution_bfs_h4, expanded_bfs_h4 = puzzle.best_first_search(puzzle.h4_linear_conflict)\n",
    "    time_bfs_h4 = time.time() - start_time\n",
    "    path_length_bfs_h4= len(solution_bfs_h4)\n",
    "\n",
    "    # A* Search with h1 (misplaced tiles)\n",
    "    print(\"Running A* Search (h1: Misplaced Tiles)...\")\n",
    "    start_time = time.time()\n",
    "    solution_astar_h1, expanded_astar_h1 = puzzle.a_star_search(puzzle.h1_misplaced_tiles)\n",
    "    time_astar_h1 = time.time() - start_time\n",
    "    path_length_astar_h1 = len(solution_astar_h1)\n",
    "\n",
    "    # A* Search with h2 (Manhattan distance)\n",
    "    print(\"Running A* Search (h2: Manhattan Distance)...\")\n",
    "    start_time = time.time()\n",
    "    solution_astar_h2, expanded_astar_h2 = puzzle.a_star_search(puzzle.h2_manhattan_distance)\n",
    "    time_astar_h2 = time.time() - start_time\n",
    "    path_length_astar_h2 = len(solution_astar_h2)\n",
    "\n",
    "    # A* Search with h3 (nb_tiles row +col)\n",
    "    print(\"Running A* Search  (h3 nb_tiles row +col)...\")\n",
    "    start_time = time.time()\n",
    "    solution_astar_h3, expanded_astar_h3 = puzzle.a_star_search(puzzle.h3_row_column_mismatch)\n",
    "    time_astar_h3 = time.time() - start_time\n",
    "    path_length_astar_h3 = len(solution_astar_h3)\n",
    "\n",
    "    # A* Search with h3 (nb_tiles row +col)\n",
    "    print(\"Running A* Search  (h4 : Manhattan + linear conflict)...\")\n",
    "    start_time = time.time()\n",
    "    solution_astar_h4, expanded_astar_h4 = puzzle.a_star_search(puzzle.h4_linear_conflict)\n",
    "    time_astar_h4 = time.time() - start_time\n",
    "    path_length_astar_h4 = len(solution_astar_h4)\n",
    "\n",
    "\n",
    "    return {\n",
    "        \"ucs\": {\"time\": time_ucs, \"expanded\": len(expanded_ucs_order), \"path_length\": path_length_ucs},\n",
    "        \"bfs_h1\": {\"time\": time_bfs_h1, \"expanded\": expanded_bfs_h1, \"path_length\": path_length_bfs_h1},\n",
    "        \"bfs_h2\": {\"time\": time_bfs_h2, \"expanded\": expanded_bfs_h2, \"path_length\": path_length_bfs_h2},\n",
    "        \"bfs_h3\": {\"time\": time_bfs_h3, \"expanded\": expanded_bfs_h3, \"path_length\": path_length_bfs_h3},\n",
    "        \"bfs_h4\": {\"time\": time_bfs_h4, \"expanded\": expanded_bfs_h4, \"path_length\": path_length_bfs_h4},\n",
    "        \"astar_h1\": {\"time\": time_astar_h1, \"expanded\": expanded_astar_h1, \"path_length\": path_length_astar_h1},\n",
    "        \"astar_h2\": {\"time\": time_astar_h2, \"expanded\": expanded_astar_h2, \"path_length\": path_length_astar_h2},\n",
    "        \"astar_h3\": {\"time\": time_astar_h3,\"expanded\": expanded_astar_h3, \"path_length\": path_length_astar_h3},\n",
    "        \"astar_h4\": {\"time\": time_astar_h4,\"expanded\": expanded_astar_h4, \"path_length\": path_length_astar_h4}\n",
    "\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I then built a display function to be compare rapidly and easily each algorithms. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_benchmark_results(results):\n",
    "    print(\"\\n--- Benchmark Results ---\")\n",
    "\n",
    "    print(\"Uniform Cost Search (UCS):\")\n",
    "    print(f\"  Time: {results['ucs']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['ucs']['expanded']}\")\n",
    "    print(f\"  Path length: {results['ucs']['path_length']}\")\n",
    "\n",
    "    print(\"\\nBest-First Search (h1: Misplaced Tiles):\")\n",
    "    print(f\"  Time: {results['bfs_h1']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['bfs_h1']['expanded']}\")\n",
    "    print(f\"  Path length: {results['bfs_h1']['path_length']}\")\n",
    "\n",
    "    print(\"\\nBest-First Search (h2: Manhattan Distance):\")\n",
    "    print(f\"  Time: {results['bfs_h2']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['bfs_h2']['expanded']}\")\n",
    "    print(f\"  Path length: {results['bfs_h2']['path_length']}\")\n",
    "\n",
    "    print(\"\\nBest-First Search (h3: nb_tiles row + col):\")\n",
    "    print(f\"  Time: {results['bfs_h3']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['bfs_h3']['expanded']}\")\n",
    "    print(f\"  Path length: {results['bfs_h3']['path_length']}\")\n",
    "\n",
    "    print(\"\\nBest-First Search (h4 : Manhattan + linear conflict)):\")\n",
    "    print(f\"  Time: {results['bfs_h4']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['bfs_h4']['expanded']}\")\n",
    "    print(f\"  Path length: {results['bfs_h4']['path_length']}\") \n",
    "\n",
    "    print(\"\\nA* Search (h1: Misplaced Tiles):\")\n",
    "    print(f\"  Time: {results['astar_h1']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['astar_h1']['expanded']}\")\n",
    "    print(f\"  Path length: {results['astar_h1']['path_length']}\")\n",
    "\n",
    "    print(\"\\nA* Search (h2: Manhattan Distance):\")\n",
    "    print(f\"  Time: {results['astar_h2']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['astar_h2']['expanded']}\")\n",
    "    print(f\"  Path length: {results['astar_h2']['path_length']}\")\n",
    "\n",
    "    print(\"\\nA* Search (h3 nb_tiles row +col):\")\n",
    "    print(f\"  Time: {results['astar_h3']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['astar_h3']['expanded']}\")\n",
    "    print(f\"  Path length: {results['astar_h3']['path_length']}\")\n",
    "\n",
    "    print(\"\\nA* Search (h4 : Manhattan + linear conflict):\")\n",
    "    print(f\"  Time: {results['astar_h4']['time']:.4f} seconds\")\n",
    "    print(f\"  Nodes expanded: {results['astar_h4']['expanded']}\")\n",
    "    print(f\"  Path length: {results['astar_h4']['path_length']}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we just need to build and initial state and run the code. \n",
    "\n",
    "To be able to display all expanded node for the UCS I chose to start from a relatively easy state. \n",
    "\n",
    "You can then compare the different algorithms. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial State:\n",
      "(4, 1, 2)\n",
      "(0, 3, 5)\n",
      "(6, 7, 8)\n",
      "WARNING ! You need to enter a solvable initial state\n"
     ]
    }
   ],
   "source": [
    "# Goal state found in the homework paper\n",
    "goal_state = [[0, 1, 2], [3, 4, 5], [6, 7, 8]]\n",
    "\n",
    "#You can generate a random state but with the display of expanded nodes of the UCS it could be long\n",
    "\"\"\"initial_state = generate_random_puzzle(goal_state)\"\"\" \n",
    "initial_state=tuple(map(tuple,[[4, 1,2], [0, 3, 5], [6, 7, 8]]))\n",
    "\n",
    "print(\"Initial State:\")\n",
    "for row in initial_state:\n",
    "    print(row)\n",
    "# Run benchmark\n",
    "if(is_solvable(initial_state)==True):\n",
    "    results = run_benchmark(initial_state, goal_state)\n",
    "    print_benchmark_results(results)\n",
    "else: \n",
    "    print('WARNING ! You need to enter a solvable initial state')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will do a real benchmark analysis after. This code just shows that we can display all of UCS expanded nodes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the questions we need to answer from the homework : \n",
    "\n",
    "Implement the Best-First Search algorithm using both the h1 and h2 heuristics, and compare their performance.\n",
    "\n",
    "Implement Best-First Search with this heuristic. Is this heuristic admissible? Why or why not? Is\n",
    "it better than the heuristics above?\n",
    "\n",
    "Implement A* Search using heuristics h1 and h2. Compare their performances.\n",
    "\n",
    "Compare Uniform Cost Search and A* Search in terms of performance and solution optimality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We redefine the run_benchmark to not display all of UCS expanded nodes to be able to test the algorithms with differents initial states. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_benchmark(initial_state, goal_state):\n",
    "    puzzle = EightPuzzle(initial_state, goal_state) #Instantiate an EightPuzzle object\n",
    "\n",
    "    # Uniform Cost Search (UCS) Specific code as it is asked to display all expanded nodes. \n",
    "    print(\"Running Uniform Cost Search (UCS)...\")\n",
    "    start_time = time.time()\n",
    "    solution_ucs, expanded_ucs_order = puzzle.uniform_cost_search()\n",
    "    time_ucs = time.time() - start_time\n",
    "    path_length_ucs=len(solution_ucs)\n",
    "    print(f\"UCS - Path length: {len(solution_ucs)}\")\n",
    "    print(f\"UCS - Time taken: {time_ucs:.4f} seconds\")\n",
    "    \n",
    "\n",
    "    # Best-First Search with h1 (misplaced tiles)\n",
    "    print(\"Running Best-First Search (h1: Misplaced Tiles)...\")\n",
    "    start_time = time.time()\n",
    "    solution_bfs_h1, expanded_bfs_h1 = puzzle.best_first_search(puzzle.h1_misplaced_tiles)\n",
    "    time_bfs_h1 = time.time() - start_time\n",
    "    path_length_bfs_h1 = len(solution_bfs_h1)\n",
    "\n",
    "    # Best-First Search with h2 (Manhattan distance)\n",
    "    print(\"Running Best-First Search (h2: Manhattan Distance)...\")\n",
    "    start_time = time.time()\n",
    "    solution_bfs_h2, expanded_bfs_h2 = puzzle.best_first_search(puzzle.h2_manhattan_distance)\n",
    "    time_bfs_h2 = time.time() - start_time\n",
    "    path_length_bfs_h2 = len(solution_bfs_h2)\n",
    "\n",
    "    # Best-First Search with h3 (nb_tiles row +col)\n",
    "    print(\"Running Best-First Search (h3: nb_tiles row + col)...\")\n",
    "    start_time = time.time()\n",
    "    solution_bfs_h3, expanded_bfs_h3 = puzzle.best_first_search(puzzle.h3_row_column_mismatch)\n",
    "    time_bfs_h3 = time.time() - start_time\n",
    "    path_length_bfs_h3= len(solution_bfs_h3)\n",
    "\n",
    "    # Best-First Search with h3 (nb_tiles row +col)\n",
    "    print(\"Running Best-First Search (h4 : Manhattan + linear conflict)...\")\n",
    "    start_time = time.time()\n",
    "    solution_bfs_h4, expanded_bfs_h4 = puzzle.best_first_search(puzzle.h4_linear_conflict)\n",
    "    time_bfs_h4 = time.time() - start_time\n",
    "    path_length_bfs_h4= len(solution_bfs_h4)\n",
    "\n",
    "    # A* Search with h1 (misplaced tiles)\n",
    "    print(\"Running A* Search (h1: Misplaced Tiles)...\")\n",
    "    start_time = time.time()\n",
    "    solution_astar_h1, expanded_astar_h1 = puzzle.a_star_search(puzzle.h1_misplaced_tiles)\n",
    "    time_astar_h1 = time.time() - start_time\n",
    "    path_length_astar_h1 = len(solution_astar_h1)\n",
    "\n",
    "    # A* Search with h2 (Manhattan distance)\n",
    "    print(\"Running A* Search (h2: Manhattan Distance)...\")\n",
    "    start_time = time.time()\n",
    "    solution_astar_h2, expanded_astar_h2 = puzzle.a_star_search(puzzle.h2_manhattan_distance)\n",
    "    time_astar_h2 = time.time() - start_time\n",
    "    path_length_astar_h2 = len(solution_astar_h2)\n",
    "\n",
    "    # A* Search with h3 (nb_tiles row +col)\n",
    "    print(\"Running A* Search  (h3 nb_tiles row +col)...\")\n",
    "    start_time = time.time()\n",
    "    solution_astar_h3, expanded_astar_h3 = puzzle.a_star_search(puzzle.h3_row_column_mismatch)\n",
    "    time_astar_h3 = time.time() - start_time\n",
    "    path_length_astar_h3 = len(solution_astar_h3)\n",
    "\n",
    "    # A* Search with h3 (nb_tiles row +col)\n",
    "    print(\"Running A* Search  (h4 : Manhattan + linear conflict)...\")\n",
    "    start_time = time.time()\n",
    "    solution_astar_h4, expanded_astar_h4 = puzzle.a_star_search(puzzle.h4_linear_conflict)\n",
    "    time_astar_h4 = time.time() - start_time\n",
    "    path_length_astar_h4 = len(solution_astar_h4)\n",
    "\n",
    "\n",
    "    return {\n",
    "        \"ucs\": {\"time\": time_ucs, \"expanded\": len(expanded_ucs_order), \"path_length\": path_length_ucs},\n",
    "        \"bfs_h1\": {\"time\": time_bfs_h1, \"expanded\": expanded_bfs_h1, \"path_length\": path_length_bfs_h1},\n",
    "        \"bfs_h2\": {\"time\": time_bfs_h2, \"expanded\": expanded_bfs_h2, \"path_length\": path_length_bfs_h2},\n",
    "        \"bfs_h3\": {\"time\": time_bfs_h3, \"expanded\": expanded_bfs_h3, \"path_length\": path_length_bfs_h3},\n",
    "        \"bfs_h4\": {\"time\": time_bfs_h4, \"expanded\": expanded_bfs_h4, \"path_length\": path_length_bfs_h4},\n",
    "        \"astar_h1\": {\"time\": time_astar_h1, \"expanded\": expanded_astar_h1, \"path_length\": path_length_astar_h1},\n",
    "        \"astar_h2\": {\"time\": time_astar_h2, \"expanded\": expanded_astar_h2, \"path_length\": path_length_astar_h2},\n",
    "        \"astar_h3\": {\"time\": time_astar_h3,\"expanded\": expanded_astar_h3, \"path_length\": path_length_astar_h3},\n",
    "        \"astar_h4\": {\"time\": time_astar_h4,\"expanded\": expanded_astar_h4, \"path_length\": path_length_astar_h4}\n",
    "\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then code a function to run multiple random initial state and then get the global statistics. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 1 - Initial state:\n",
      "[7, 5, 6]\n",
      "[2, 8, 4]\n",
      "[1, 0, 3]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 23\n",
      "UCS - Time taken: 3.8795 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 2 - Initial state:\n",
      "[3, 4, 8]\n",
      "[2, 7, 1]\n",
      "[6, 5, 0]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 22\n",
      "UCS - Time taken: 2.2447 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 3 - Initial state:\n",
      "[2, 1, 5]\n",
      "[0, 7, 6]\n",
      "[4, 8, 3]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 21\n",
      "UCS - Time taken: 1.7157 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 4 - Initial state:\n",
      "[6, 3, 4]\n",
      "[2, 5, 1]\n",
      "[8, 0, 7]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 21\n",
      "UCS - Time taken: 1.6700 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 5 - Initial state:\n",
      "[5, 2, 4]\n",
      "[8, 3, 0]\n",
      "[1, 6, 7]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 23\n",
      "UCS - Time taken: 3.3710 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 6 - Initial state:\n",
      "[4, 0, 5]\n",
      "[8, 7, 1]\n",
      "[3, 2, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 25\n",
      "UCS - Time taken: 5.2736 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 7 - Initial state:\n",
      "[4, 7, 2]\n",
      "[3, 0, 1]\n",
      "[8, 5, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 18\n",
      "UCS - Time taken: 0.5950 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 8 - Initial state:\n",
      "[6, 7, 4]\n",
      "[2, 3, 5]\n",
      "[0, 1, 8]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 24\n",
      "UCS - Time taken: 4.2060 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 9 - Initial state:\n",
      "[6, 5, 4]\n",
      "[2, 1, 3]\n",
      "[8, 7, 0]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 24\n",
      "UCS - Time taken: 4.5650 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 10 - Initial state:\n",
      "[5, 3, 8]\n",
      "[1, 2, 6]\n",
      "[0, 4, 7]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 24\n",
      "UCS - Time taken: 3.8470 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 11 - Initial state:\n",
      "[6, 1, 5]\n",
      "[8, 7, 4]\n",
      "[3, 0, 2]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 21\n",
      "UCS - Time taken: 2.4750 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 12 - Initial state:\n",
      "[7, 8, 6]\n",
      "[0, 2, 1]\n",
      "[5, 3, 4]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 25\n",
      "UCS - Time taken: 5.5982 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 13 - Initial state:\n",
      "[5, 4, 8]\n",
      "[2, 0, 3]\n",
      "[1, 6, 7]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 18\n",
      "UCS - Time taken: 0.6870 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 14 - Initial state:\n",
      "[2, 3, 5]\n",
      "[4, 1, 7]\n",
      "[6, 8, 0]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 18\n",
      "UCS - Time taken: 0.5195 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 15 - Initial state:\n",
      "[2, 7, 5]\n",
      "[8, 6, 1]\n",
      "[0, 3, 4]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 22\n",
      "UCS - Time taken: 2.4410 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 16 - Initial state:\n",
      "[1, 0, 5]\n",
      "[7, 8, 3]\n",
      "[2, 4, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 25\n",
      "UCS - Time taken: 5.6680 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 17 - Initial state:\n",
      "[0, 5, 1]\n",
      "[8, 3, 7]\n",
      "[4, 2, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 20\n",
      "UCS - Time taken: 1.2025 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 18 - Initial state:\n",
      "[7, 2, 4]\n",
      "[5, 0, 1]\n",
      "[8, 6, 3]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 24\n",
      "UCS - Time taken: 4.6140 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 19 - Initial state:\n",
      "[5, 3, 1]\n",
      "[7, 4, 0]\n",
      "[8, 2, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 25\n",
      "UCS - Time taken: 4.9040 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 20 - Initial state:\n",
      "[8, 1, 2]\n",
      "[6, 0, 4]\n",
      "[3, 7, 5]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 18\n",
      "UCS - Time taken: 0.6800 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 21 - Initial state:\n",
      "[2, 7, 0]\n",
      "[4, 6, 8]\n",
      "[1, 3, 5]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 20\n",
      "UCS - Time taken: 1.3446 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 22 - Initial state:\n",
      "[6, 1, 8]\n",
      "[3, 2, 0]\n",
      "[5, 4, 7]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 23\n",
      "UCS - Time taken: 3.0980 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 23 - Initial state:\n",
      "[3, 2, 7]\n",
      "[1, 4, 0]\n",
      "[5, 8, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 23\n",
      "UCS - Time taken: 3.4700 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 24 - Initial state:\n",
      "[6, 1, 3]\n",
      "[7, 4, 0]\n",
      "[5, 8, 2]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 21\n",
      "UCS - Time taken: 1.8445 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 25 - Initial state:\n",
      "[6, 3, 8]\n",
      "[0, 7, 1]\n",
      "[4, 5, 2]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 23\n",
      "UCS - Time taken: 3.2420 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 26 - Initial state:\n",
      "[4, 1, 2]\n",
      "[0, 8, 7]\n",
      "[6, 3, 5]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 19\n",
      "UCS - Time taken: 0.8450 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 27 - Initial state:\n",
      "[4, 8, 6]\n",
      "[0, 3, 7]\n",
      "[5, 1, 2]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 25\n",
      "UCS - Time taken: 4.6561 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 28 - Initial state:\n",
      "[4, 5, 2]\n",
      "[1, 8, 6]\n",
      "[7, 3, 0]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 16\n",
      "UCS - Time taken: 0.1780 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 29 - Initial state:\n",
      "[6, 8, 4]\n",
      "[1, 0, 3]\n",
      "[2, 7, 5]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 24\n",
      "UCS - Time taken: 4.0585 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 30 - Initial state:\n",
      "[6, 7, 5]\n",
      "[2, 1, 8]\n",
      "[4, 3, 0]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 22\n",
      "UCS - Time taken: 2.5200 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 31 - Initial state:\n",
      "[5, 8, 4]\n",
      "[3, 0, 7]\n",
      "[6, 1, 2]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 20\n",
      "UCS - Time taken: 1.2750 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 32 - Initial state:\n",
      "[0, 3, 5]\n",
      "[6, 4, 7]\n",
      "[2, 8, 1]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 22\n",
      "UCS - Time taken: 2.5216 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 33 - Initial state:\n",
      "[4, 8, 3]\n",
      "[0, 2, 5]\n",
      "[7, 6, 1]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 23\n",
      "UCS - Time taken: 3.2191 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 34 - Initial state:\n",
      "[1, 3, 4]\n",
      "[7, 5, 0]\n",
      "[2, 6, 8]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 19\n",
      "UCS - Time taken: 0.8480 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 35 - Initial state:\n",
      "[5, 8, 0]\n",
      "[4, 7, 3]\n",
      "[2, 1, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 26\n",
      "UCS - Time taken: 5.1002 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 36 - Initial state:\n",
      "[8, 7, 4]\n",
      "[5, 6, 1]\n",
      "[0, 2, 3]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 28\n",
      "UCS - Time taken: 6.1221 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 37 - Initial state:\n",
      "[8, 6, 0]\n",
      "[4, 7, 2]\n",
      "[5, 1, 3]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 26\n",
      "UCS - Time taken: 5.5725 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 38 - Initial state:\n",
      "[7, 8, 0]\n",
      "[4, 2, 3]\n",
      "[6, 5, 1]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 22\n",
      "UCS - Time taken: 2.2951 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 39 - Initial state:\n",
      "[6, 7, 3]\n",
      "[2, 4, 8]\n",
      "[1, 5, 0]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 26\n",
      "UCS - Time taken: 5.1270 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 40 - Initial state:\n",
      "[2, 5, 8]\n",
      "[3, 7, 4]\n",
      "[1, 0, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 19\n",
      "UCS - Time taken: 0.7835 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 41 - Initial state:\n",
      "[8, 0, 1]\n",
      "[4, 2, 5]\n",
      "[3, 6, 7]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 19\n",
      "UCS - Time taken: 0.7527 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 42 - Initial state:\n",
      "[0, 6, 1]\n",
      "[8, 4, 3]\n",
      "[2, 7, 5]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 24\n",
      "UCS - Time taken: 3.7267 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 43 - Initial state:\n",
      "[5, 8, 4]\n",
      "[1, 2, 3]\n",
      "[0, 7, 6]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 26\n",
      "UCS - Time taken: 5.0895 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 44 - Initial state:\n",
      "[5, 3, 1]\n",
      "[2, 0, 7]\n",
      "[6, 8, 4]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 18\n",
      "UCS - Time taken: 0.5880 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 45 - Initial state:\n",
      "[7, 8, 6]\n",
      "[2, 3, 0]\n",
      "[1, 5, 4]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 27\n",
      "UCS - Time taken: 5.7970 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 46 - Initial state:\n",
      "[1, 5, 6]\n",
      "[0, 4, 2]\n",
      "[3, 7, 8]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 15\n",
      "UCS - Time taken: 0.1310 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 47 - Initial state:\n",
      "[3, 1, 6]\n",
      "[2, 7, 5]\n",
      "[4, 8, 0]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 22\n",
      "UCS - Time taken: 2.1960 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 48 - Initial state:\n",
      "[7, 6, 4]\n",
      "[1, 0, 5]\n",
      "[2, 3, 8]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 20\n",
      "UCS - Time taken: 1.4300 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 49 - Initial state:\n",
      "[0, 7, 2]\n",
      "[5, 3, 8]\n",
      "[6, 1, 4]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 20\n",
      "UCS - Time taken: 1.1730 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "Trial 50 - Initial state:\n",
      "[5, 0, 3]\n",
      "[1, 7, 6]\n",
      "[4, 2, 8]\n",
      "Running Uniform Cost Search (UCS)...\n",
      "UCS - Path length: 25\n",
      "UCS - Time taken: 4.5591 seconds\n",
      "Running Best-First Search (h1: Misplaced Tiles)...\n",
      "Running Best-First Search (h2: Manhattan Distance)...\n",
      "Running Best-First Search (h3: nb_tiles row + col)...\n",
      "Running Best-First Search (h4 : Manhattan + linear conflict)...\n",
      "Running A* Search (h1: Misplaced Tiles)...\n",
      "Running A* Search (h2: Manhattan Distance)...\n",
      "Running A* Search  (h3 nb_tiles row +col)...\n",
      "Running A* Search  (h4 : Manhattan + linear conflict)...\n",
      "\n",
      "--- Average Benchmark Results (50 trials) ---\n",
      "\n",
      "UCS:\n",
      "  Average Time: 2.8744 seconds\n",
      "  Average Nodes Expanded: 102931.08\n",
      "  Average Path Length: 22.08\n",
      "\n",
      "BFS_H1:\n",
      "  Average Time: 0.0167 seconds\n",
      "  Average Nodes Expanded: 508.02\n",
      "  Average Path Length: 103.24\n",
      "\n",
      "BFS_H2:\n",
      "  Average Time: 0.0107 seconds\n",
      "  Average Nodes Expanded: 224.78\n",
      "  Average Path Length: 68.48\n",
      "\n",
      "BFS_H3:\n",
      "  Average Time: 0.0175 seconds\n",
      "  Average Nodes Expanded: 404.34\n",
      "  Average Path Length: 104.48\n",
      "\n",
      "BFS_H4:\n",
      "  Average Time: 0.0198 seconds\n",
      "  Average Nodes Expanded: 247.40\n",
      "  Average Path Length: 69.28\n",
      "\n",
      "ASTAR_H1:\n",
      "  Average Time: 0.6411 seconds\n",
      "  Average Nodes Expanded: 14933.54\n",
      "  Average Path Length: 23.08\n",
      "\n",
      "ASTAR_H2:\n",
      "  Average Time: 0.0706 seconds\n",
      "  Average Nodes Expanded: 1314.86\n",
      "  Average Path Length: 23.08\n",
      "\n",
      "ASTAR_H3:\n",
      "  Average Time: 0.2606 seconds\n",
      "  Average Nodes Expanded: 4899.60\n",
      "  Average Path Length: 23.12\n",
      "\n",
      "ASTAR_H4:\n",
      "  Average Time: 0.1697 seconds\n",
      "  Average Nodes Expanded: 1941.96\n",
      "  Average Path Length: 23.88\n",
      "\n",
      "--- Algorithm Ranking by Path Length ---\n",
      "1. UCS (Avg Path Length: 22.08)\n",
      "2. ASTAR_H1 (Avg Path Length: 23.08)\n",
      "3. ASTAR_H2 (Avg Path Length: 23.08)\n",
      "4. ASTAR_H3 (Avg Path Length: 23.12)\n",
      "5. ASTAR_H4 (Avg Path Length: 23.88)\n",
      "6. BFS_H2 (Avg Path Length: 68.48)\n",
      "7. BFS_H4 (Avg Path Length: 69.28)\n",
      "8. BFS_H1 (Avg Path Length: 103.24)\n",
      "9. BFS_H3 (Avg Path Length: 104.48)\n",
      "\n",
      "--- Algorithm Ranking by Nodes Expanded ---\n",
      "1. BFS_H2 (Avg Nodes Expanded: 224.78)\n",
      "2. BFS_H4 (Avg Nodes Expanded: 247.40)\n",
      "3. BFS_H3 (Avg Nodes Expanded: 404.34)\n",
      "4. BFS_H1 (Avg Nodes Expanded: 508.02)\n",
      "5. ASTAR_H2 (Avg Nodes Expanded: 1314.86)\n",
      "6. ASTAR_H4 (Avg Nodes Expanded: 1941.96)\n",
      "7. ASTAR_H3 (Avg Nodes Expanded: 4899.60)\n",
      "8. ASTAR_H1 (Avg Nodes Expanded: 14933.54)\n",
      "9. UCS (Avg Nodes Expanded: 102931.08)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Function to rank algorithms based on their performance\n",
    "def rank_algorithms(results, key):\n",
    "    \"\"\" Rank algorithms based on a specific key ('path_length' or 'expanded') \"\"\"\n",
    "    return sorted(results, key=lambda x: results[x][key])\n",
    "\n",
    "# Function to benchmark algorithms on 50 random puzzles\n",
    "def benchmark_algorithms(goal_state, num_trials):\n",
    "    # Dictionary to accumulate time, path length, and nodes expanded for each algorithm\n",
    "    total_metrics = {\n",
    "        \"ucs\": {\"time\": [], \"expanded\": [], \"path_length\": []},\n",
    "        \"bfs_h1\": {\"time\": [], \"expanded\": [], \"path_length\": []},\n",
    "        \"bfs_h2\": {\"time\": [], \"expanded\": [], \"path_length\": []},\n",
    "        \"bfs_h3\": {\"time\": [], \"expanded\": [], \"path_length\": []},\n",
    "        \"bfs_h4\": {\"time\": [], \"expanded\": [], \"path_length\": []},\n",
    "        \"astar_h1\": {\"time\": [], \"expanded\": [], \"path_length\": []},\n",
    "        \"astar_h2\": {\"time\": [], \"expanded\": [], \"path_length\": []},\n",
    "        \"astar_h3\": {\"time\": [], \"expanded\": [], \"path_length\": []},\n",
    "        \"astar_h4\": {\"time\": [], \"expanded\": [], \"path_length\": []}  \n",
    "    }\n",
    "\n",
    "    # Run the benchmark for the specified number of trials\n",
    "    for trial in range(num_trials):\n",
    "        initial_state = generate_random_puzzle(goal_state)\n",
    "        print(f\"Trial {trial + 1} - Initial state:\")\n",
    "        for row in initial_state:\n",
    "            print(row)\n",
    "\n",
    "        results = run_benchmark(initial_state, goal_state)\n",
    "\n",
    "        # Collect the metrics\n",
    "        for algo in total_metrics.keys():\n",
    "            total_metrics[algo][\"time\"].append(results[algo][\"time\"])\n",
    "            total_metrics[algo][\"expanded\"].append(results[algo][\"expanded\"])\n",
    "            total_metrics[algo][\"path_length\"].append(results[algo][\"path_length\"])\n",
    "\n",
    "    # Calculate average metrics and rank\n",
    "    avg_metrics = {}\n",
    "    for algo in total_metrics.keys():\n",
    "        avg_metrics[algo] = {\n",
    "            \"avg_time\": mean(total_metrics[algo][\"time\"]),\n",
    "            \"avg_expanded\": mean(total_metrics[algo][\"expanded\"]),\n",
    "            \"avg_path_length\": mean(total_metrics[algo][\"path_length\"])\n",
    "        }\n",
    "\n",
    "    # Rank algorithms based on path length and expanded nodes\n",
    "    rank_by_path_length = rank_algorithms(avg_metrics, \"avg_path_length\")\n",
    "    rank_by_expanded = rank_algorithms(avg_metrics, \"avg_expanded\")\n",
    "\n",
    "    return avg_metrics, rank_by_path_length, rank_by_expanded\n",
    "\n",
    "# Function to display benchmark results\n",
    "def display_benchmark_results(avg_metrics, rank_by_path_length, rank_by_expanded):\n",
    "    print(\"\\n--- Average Benchmark Results (50 trials) ---\")\n",
    "\n",
    "    for algo, metrics in avg_metrics.items():\n",
    "        print(f\"\\n{algo.upper()}:\")\n",
    "        print(f\"  Average Time: {metrics['avg_time']:.4f} seconds\")\n",
    "        print(f\"  Average Nodes Expanded: {metrics['avg_expanded']:.2f}\")\n",
    "        print(f\"  Average Path Length: {metrics['avg_path_length']:.2f}\")\n",
    "\n",
    "    print(\"\\n--- Algorithm Ranking by Path Length ---\")\n",
    "    for i, algo in enumerate(rank_by_path_length):\n",
    "        print(f\"{i + 1}. {algo.upper()} (Avg Path Length: {avg_metrics[algo]['avg_path_length']:.2f})\")\n",
    "\n",
    "    print(\"\\n--- Algorithm Ranking by Nodes Expanded ---\")\n",
    "    for i, algo in enumerate(rank_by_expanded):\n",
    "        print(f\"{i + 1}. {algo.upper()} (Avg Nodes Expanded: {avg_metrics[algo]['avg_expanded']:.2f})\")\n",
    "\n",
    "\n",
    "goal_state = [[0, 1, 2], [3, 4, 5], [6, 7, 8]]\n",
    "\n",
    "# Run benchmark for 50 random puzzles\n",
    "avg_metrics, rank_by_path_length, rank_by_expanded = benchmark_algorithms(goal_state,50)\n",
    "\n",
    "# Display results\n",
    "display_benchmark_results(avg_metrics, rank_by_path_length, rank_by_expanded)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OVERALL RESULTS FOR 50 RANDOM INITIAL STATES :"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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uOvnSntvhe27Coz0dGN9HT4fN14/OVw3HD3Da40Jwv+RMOPOgS39lL+3vnrtLJ/WExS9U9KrLcXcZoesxy18Xb2LJ5yPNbYcJmxWGxJvP6HZj5i7ljvhEB25UeUfmyCifOxvkTHJZq8oHNp0nLqd9P8PkUfVDDhvuT3Nh0B5yPpKTbt9lZ/7eTW7b3GgEIlz+VJcxhHUSnyEZdvBZ+ZJdDg1yGt13te+H7gw2bPqhxI5wd1i7g0msjht7Gtn3GDXXusvt5ivcrusXnfwoX9LVWGEkLsdHbjqfqzw5lpzLv/thXl2yVd48ZxWGCm/ns6pz5k74PGdHfRK35KvY2N+NxEOecqRONJXc13PlH/kqB2ASdrfneehkJF/JIS+/FR72Z3zvhub13zY3F575n8TRwb23SR7JZ3e5cbmsLoIj9kfmz5pWuVB+deEq375P01B9fH3m63zekx9eHCbnj8vxPfX5brrT3E7+4eTPuNw4zNXbMf6nuT32oHcvMXxanYv2sfn3C1Ncn09tn5dvz/0zzqe5nWxuKvZnfHrS5ZkHmqaX689IwO+OufvkprpUn+i+ezzPio+zlp+gnzWewf34Jj3N7Y7mJoLq8qs+WV1JXi5S/+8Xj/Z5Jf5nt0WD8/x/xq+knz1vV+HnZU51uMrm2Hl8c/nqHE9zu7O5fXUBx//rH9Kp8dR4OHA7B6a5TXObt+HhwHBgOPByHJjmNqR+OVLPW+7tb7mTs8nZq3Fgmts0t2luw4HhwHDg5TgwzW1I/XKkfrU30IlnPlUNB27nwDS3aW7T3IYDw4HhwMtxYJrbkPrlSD1vube/5U7OJmevxoFpbm/e3PSl2PnOVn+x8ZdI5jtWf8+RvnM537Hs+VI1iPme3m35qnJ4Zm2a2xs3t/kTXn/+4e3uL1+8W3PbNa/d/plL6B105i+sfH6DO9Tc8i80fNabG35Xnyzyr3fomcMCofwvS/i8+vNVK580A7eh+Zm3eulUceEjbfL2d9YfOWHk0vZ8scdI/qo8IfOZI7nJ/K9i2OHD5mc1N/xlfXc4P2tfuVyd793+o3DKr9c9aw6fXeZe3qpGbi99KlY/l8h2+ZO9ezE9Kr+vaHfb3FQQLxYk8rVHJAbS/Pz586MJ5OXDfjYIyVUXB/IVQcGPTOeTi8mxcAAqn9itRskndsnhw+1prkOh/0+dRt+rbB9Z6/y7rnL1+++/f9T/Cp9u+8yc3Hj+WatyecQH+m7T9eD7VfHj7yp7jvWKuWq+Otu7/SswpA351A/r5NDX2PNR+2ebSepWPuGG42CtyiH3S7XnuGd+zae8bXOrEq2DeZY0lb1qTWTShaVR5HECSV6Xkd6UukspbUKstONyO58Q3H2uyOy2c64cVhcyPrj85IvDkHtp8+gzmPFR6SEj/5IDA7Ja7/KvHHts5J43Wx9XGPDFSPyef+2BxW1VPn1fGB1HzvFBHqSrH+Q8PvAdGYnBsXR67k9+U0fPqssvv/zykW+wpZzsd/FqHUzo5+i1l7yef/311487AFnylbEQQ7ef8kefhWNXA+K61XenJzt+7+Uz2BVzh006ytmtmLA94/HG922bGwdXl5SIkGSBJNVBrgjAZadDUe1rbeezIj2X38pu5a87APio4lrtVT66NeXOD2kl5zmXX+VfI7Jd3KyDn7z7Bam9Mwec+IUNHBpZx6fW9Onb8XZ8QTdtYp94hJcYiOnWmndY8eVjXt7g9BjJo9eSOD2etIWM28K3ZImTNR+1r1y4T9nJ8ykd8iR56bmde+cZU2WPnHkuKrlcq+LxWMgbeUz7qxzCp6vzkTHM8z/97VRzO0Kse5ILkSBRRVJk8qB1fpHvSMX+ymeFQ/aEIQne4WC9OkDawwc4kN/tudxuLsyrC0z6kiFXHMjEpP281JQHv/iIx/ODPezv8LJf2dKebO9qQH0z7s4mPsGael390OtG/GUuXR4Zz5n206eeM27wYj+fZafLhfZUk4zVsWnf66u9Dq/2Koxu78x8hR97R2SQzTFzQA5//PjxkRvnreaqAfmu8rOzn/vzfPzT2SpXNzc3LhIv8MrBmT0dFv+kAFErn+ARwZxk6XdlQ7JHfHKI8aUxL/f02z1z6N2Wzzksro//as/lVvNdHqTLYfbLVbnPSw88Kznq4zLYvzWOyh9rFTcyD0djcL0Oq7CfqT14V7F3tpVDbyyVXOKt/K04UOXI81Ht48Nr7DpXzxW3zkrmkLg4R2fqI6weo+cc+9r3mCRzi8+qbm5v5l/Q3ChiXnJXF6Mqvtb8YKdPiCeSVfjYT2Ji54jPPMTSqQ4ZNldj5U/y+NB+6q/2UrZ73uVBen6gsUPtNbKWtrhYKxmviWJb1RL7ORI/Fwmj+0Onk3UckkWusqF9Ysp6dPXDfzfiL+25vDhKbDl63ioMFV7Z84tescpuFbNkM0eJLfeJqbLnulfMFbOwd+fYfRDnKtcuz5wc6JOa5y35LnnJkkv29bzyWdUN3zNe09iUx8Of3CCwF/sRhXCCiCT5syKN8Ggfsjk+7FaHgr30xTM+yQGHGL0zOekIjg98egyrPZdbzcFc5QE9Dizx+5h6HofykrngsnUbfkHj88hI/OS/00Euser51osZ/FkPj7vDUa2DLe257FHblVzipd6ef827HFY5cmzVPjF1Nl3/nrnsC3vWcGWzwruS157yWvnJ3CKXccvniuNV3XaYZv/2pneouUHevLiqhKuwIoYKWO3v1vCVhOGQ7ojdEQ594UsMR31Wchy4W+PtCI6Pyt5qL2NaPa8OfB5gtyO95ADyyoP2M79dnG736Jz4kxupL5/V5VLFDf4q37Lb7Z+Nixg6f/Kp+Cr8VZxdPbB/1Ba2d3FVOSSmqi6yt2qm+N2Nsl01nJ1ehVc6YM78+V7Gk7mU7apOu5g7TLtYZv+2BrdtbisSZLK5CM6QEFurw6U9yKR5kg//VQNcNbejPsmF+8VudUiIqRo7n/jQfuqt9lJ29ZyH1GV3e9VFxWH9448/Pi6No/Zc7sic+D3/lZ72hZMcUqOKl+x19YNT2MJfVz/2u5EY0p7L7zAhW2FIvPjb5QybmTvWGam1MLLW+SAO5V16yN86gqk61ytbyk/FV+mw1+0Lr3OCGL1u4PLYyL/rOkb2Xcf3Z35bA1vla9vcVAQRoPqpyIa8k2AFwPc4DF3hk2D4cmyd3852tw4u98k8LwpI3vnGlo+SrQ4APrDFs8fInEbvdo/MOWD4cB3ltKqrZNDL+hB/p1fVSTGkHcdRzclF5r+SVWzkSaN0utiIK+U95syVnqv6VVh8jRjcF/P0UeXNc1ZhIBa3pTk+fOzqlfIuV+WQmKq6YKva87x0c86n4/Y5+QCD7znutI/8qoaZf88p9hSX+9R85VfyZ88tPmc81gC3zW0SeSyRz5YnHdTPOGS6ICo/XArVhfFsufzOeLvmwuVOc/jOMbwKNhr15Pxz7tRpbm/6h5N5w1+9Zd57qXCYKx9crtPcHnvQdZFWn06o/1y0j82/n6HPeqF0n+88n+b2ps1NpKfBPPKCk+385EbTy/V3PoiPir375Ka66FdoZ39d+Ci8r2qX31RMvj/vZWKa24XNjbfh/B18PlefZL7qUOuwVW/2V+LhIvU8fKccXBnrd7RFg/P8P7rm3zEPX4WJl7n5LcXnNTbVeprbhc3tqw7P+P3cQzP5nnwPB74/B6a5TXM7/U+054B//wM+NZoavSsHprlNc5vmNhwYDgwHXo4D09yG1C9H6nd9U52451PacOBPDkxzm+Y2zW04MBwYDrwcB6a5DalfjtTz9vrn2+vkYnLxrhyY5jbNbZrbcGA4MBx4OQ5Mc3tzUn/G99ye+c2R7y7Od5T+/glI31mc7yje9mlwvud2W76uui+mub1xc+MvlLzzxU0Our8c8W7Nbde8dvtXXUyvZkf80pfoO569WrzfIZ5tc6Mo/tcNPuvNjb+ssPprCvnXL/RMYivsHkf1559WPrkI3YbmZ5qDdKq48OE2WcNvhZuYj45c2p6v1CV/V/hL22eeMw/kYxXDzg82u0uHPHk9djZX+/i7yt7K15k95XJ1vnf7Z3we0ZFf6q0xa06dXOZe3qpGbi99Cjefylyuy5/s3YvpSK5G5u+fFLfNLRMFiboCpvzZZ0jz8+fPjyaQlw/72SAkV10cyFcEBSMynU8uJsfCAah8YrcaJZ/YJYcP7OlZchqxoxjuPSSdf3xolJ/ff//947IDj+9/9pzceP5Zq3J5BB/6btP14PtV8ePvKnuO9Yq5ar4627v9KzCkDfnUD+vk0NfY81H7Z89J6lY+4YbjYK3KIfdLtee4Z37NrzFvbm5K/JGL8d4CiUxc6iKPE0i2dRnpbam7lNI/xEo7LrfzCcHd54rMbjvnXQ7xsbr8jsikP38G88oHMopVcnkgV/lXjr3ZkHt/u2W+wuCYNSduz7/WweK2Kp++L4xgqEZ8kAfp6gdZjy9xrp6JwbF08u5PflNHz6rLL7/88pFvsKWc7Hfxah1M6OfotZe8nn/99dePxoEs+cpYiKHbT/mjz8KxqwFx3eq705Mdb5b5DHbF3GGTjnJ2KyZsz3i88X3b5sbB1SUlIiRZIEl1kCsCcNnpUFT7Wtv5rEjP5beyW/nrDgA+VnEdkal8sqbc+SFl3UfPufwp/xqR6eJmHfzk3S9I7Z054MQtbODQyDo+taZP34634wu6aRP7xCO8xEBMt9a8w4ovH/PyBqfHSB69lsTp8aQtZNwWviVLnKz5qH3lwn3KTp5P6ZAnyUvP7dw7z5gqe+TMc1HJ5VoVj8dC3shj2l/lED5dnY+MYZ5P/OFkCEOBH5FEiIQPfDqJkMmD1uFBviMV+yufFQ7ZEwbH1mHwdfmpLgR8gMN1mHeHiv3duDp86EqGXHEgE5P2MwZh84uPeDw/2MM+PndjZUs6R/JBffPi7myCBayp19UPvW7EX+bS5ZHxnGk/feo5uQde7Oez7HS50J5qkrE6Nu17fbXX4dVehdHtnZmv8GPviAyyOWYOyOGPHz8+cuO81Vw1IN9Vfnb2c3+ej386W+Xq0Cc3yKsi6seLuzJ+dk/+/JMCRK38crGBDZKl75UNyR7xmXmQz7zc02/3zKEHd45dHBy0s353eRBefPjlqtznpUc+VnLUx2Ww38XY5azyx1rFjbRzNAbX67AK+5kagHcVe2dbOfTGUskl3srfigNVjjwf1T4+vMauc/Vcceu8ZA6Ji7N0pj7C6jF6zrGvfY9JMrf4rOrm9mb+ic0tk63i+iHL/Xufq+JrbeUT4olkeQkLD/tJTLAe8ZmHWDrVIcPmaqz8SR4f2k99Lq5VHlInn3d5kLwfaPQ5wBpZS1vgq2S8JortTAzkhouE0f2BrZN1HJJFrrKhfWLKenT1w3834i/tubw4Smw5et4qDBVe2fOLXrHKbhWzZDNHiS33iamy57pXzBWzsHfn2H0Q5yrXLs+cHOiTmuct+S55yZJL9vW88lnVDd8zXtPYlMdDn9wy4dUBSpmzz04QkSR/VqSRT+1DNseA3epQsJe+eMZnHmL0/AC4z9W8Izg+8IkNfFWxIXNkxE6VB/Q5sMTvY+p5HLpMMhdwxW34BY3PIyO52V2iyCVWPd96MYM/6+FxH8GODNjSHvsaj9qu5BIv9fb8a97lsMqRY6v2iamz6fr3zGVf2LOGK5sV3pW89pTXyk/mFrmMWz5XHK/qtsM0+7c3vcubmworYqiAZwrSHRQO6Y7YHeHQF77EddRnJceBuzXejuD4cHtgX11KGdPqeXXg8wC7Hel1zUt50H7mt4vT7R6dk5u8TFJfPqvLpYp7Fa/sdvtn4yIGr2/iV3wV/pSrMCTeo7awXdlkT2OVQ2Kq6iJ7V/BWtquG49iqeYVXcmBOPvtexpO5lO2qTruYO0wV/lm7vamRs5ubGxdtRQoO1hkSAmh1uLQHmTRP8uG/aoDgFrHwxXjUJwfC/WK3ygf2q7HziQ/tSw/7VzIyhE8AACAASURBVFwQ4MhDyrrG3V6Fg8P6xx9/fFwaR+253JE5ufH8V3raF84qh8kN8tvVD05hC39d/djvRmJIey6/w4RshSHx4m+XM2xm7lhnpNbCyFrngzhUi+rcob8bwZS12+kpPxVfpcdety+8zgli9LqBy2Mj/67rONl3Hd+f+flmlrnbNjcngYigHy9wGlTRdjKpwzOHoSt8Egxf4Fr57Wx362Byn8zzooDkq7xgj1Gy1QHAB7aw7TEyp9Fj8+jIAcOH6ymn3SWCXtYHjJ1eVSfFkHYcRzUnN5n/SlaxkSeN0uliI66Ul132Mld6rupXYfE1YnBfzNNHlTfPWYWhwis5fPjY1SvlXa7KITFVdcFWted56eacT8ftc/IBBt9z3Gkf+VUNM/+KJe0oLvep+cqv5M+e2/Q9z+tGuG1uk8B1Ap81Pzqon3HIdEFUfrgUqgvjWXP6HXF3zYXLnebwHbG/GiYa9eT8c+7UaW5v+oeTecNfvWXee7lwmCsfXK7T3B570HWRVp9OqP9ctI/Nv5+hz3qhdJ/vPJ/m9qbNTaSnwTzygpPt/ORG08v1dz6Ij4q9++SmuuhXaGd/XfgovK9ql99UTL4/72VimtuFzY234fwdfD5Xn2S+6lDrsFVv9lfi4SL1PHynHFwZ63e0RYPz/D+65t8xD1+FiZe5+S3F5zU21Xqa24XN7asOz/j93EMz+Z58Dwe+PwemuU1z+4d/ATYH9/sf3KnR1Gg4sObANLdpbtPchgPDgeHAy3FgmtuQ+uVIPW+06zfayc/k5x04MM1tmts0t+HAcGA48HIcmOY2pH45Ur/DW+nEOJ++hgNrDkxzm+Y2zW04MBwYDrwcB6a5vTmpP+N7bs/8hsl3F+c7Sn9/S9Z3Fuc7iutPDMn3+Z7bbfnK/J19nub2xs2Nv1Dyzhc3Oej+csS7Nbdd89rtn72IXl1P/NKX6DuevXr8XxHfTc2Ng64ifcaFKB/ytfprCvnXL/RMIiGU/2UGn1d//mnlk4vQbWh+JhfSqeLCBzY95/itcBPz0RG7nq/UJX9X+EvbZ57JDXlgXMWw84PN7tIhT9RjZ2+3j7+r7O383bqvXK4+me32b/V3VF5+qbfGrDl1cpkreIvf9Adu6onflU/VfLWPzRmv+aR3U3Oj0Crkow8nH+V//vz50QTy8mE/G4TkKmzIdyQVoZDpfEJkxyJfZ/IhvcQuDPioYoD0iuHeQ9L5x4dG+fn9998/LrsVHtd55JzceP5Zq3J5BAv6btP1uDSvih9/V9lzrFfMVfPv1tyEST/ERw59jT0ftX/2nIgPOte//fbbxzmtfAmHeKcRvyuf3C+r/GJnxvsb3OHmBqEo9qMPpxNHhElyQb7uUkpyQKy043I7n+TAfXL53UpY5a+6kPGxyi8yjsPj2M3BvPKBjHxILuPTug5/hUE59tjIveTzZ4Uh4+jiBovbqnz6vjAmFn8mLvIgXf0g4/ElztUzMTiWTt79yW/q6Fl1+eWXXz7yDbaUk/0uXq2DCf0cvfaS1/Ovv/760TiQJV8ZCzF0+yl/9Fk4djUgrlt9S0//413VnvrL3xFs+KxqIH1hUc5uxXTE98j8tSEeam5cFCowxe6Kd1WCZZ9DJSIkkSHJURweQ4dx5xPiOjHJx1Hy41u+Mibt4WMVFzKOA7tHRunt3mglAz7501wj9ru4WQc/eaeW0tfemQPexc06PuVDn74dr+KRT5eRHLpdLolHusRATLfW3P0lDu35j2yT/06PPHotidPjSVvIVBgkS5yOh7n2lQv3KTuOFVnyJHnpsX7FmDFVNne1rXRyjfofxY/PKreyfau9xDPPfz0nq3wcam5OXorTFW/l7OgehwIfEMYPLDJ50DofyHckZX/ls8Ihe8Lg2DoMvu459XV8gMP3NAfn6gJKnXwW5p2+ZMhVV3Pt56WmPPjFRzyeH+xhP/F1z5Utycr2rgZd3jqbYABr5qurH3rdiL+uvtJDxnOm9fSp54wbvNjPZ9npcqE91SRj1To/2vf6ar3Dq70KI7bOjiv82Dwig+xqJH9HuXqEi7scr/DM3p9c3OVi29wo7uqw7Jzcuq/D4p8UIGpFMMikQ64fcKbPlQ3JHvHJIcaXxrzc02/3zKF3Wz73OMDO/lmfwoKtKpdgpeZ+uVYHknys5KiPy2DfY8T3aqz8sbaKB5tHY0BeY4dV2M/UAbyr2DvbyqE3lkou8Vb+VhyocuT5qPbx4TV2navniltnIXNIXFecEzCTzyP8QnbHi6pu+JvxePPa5Wrb3JLMFDCJtXN0y35VfK35wU57TuzqzZP9jqRHfOYhlk51yBJb9Vz5kxw+tF/paY2GsZLpdHd5wH7mGp9+gaUtuFHJeE2EO+13eH2d3HB5Mbo/5DtZxyFZ5Cob2iemzLWed5cYWHzEX9pzGXGU2HL0vFUYKryy51gVq+xWMed5d1yaV/vEVNlL/XufFbOwC8fOFnGucr2zQT53/pDz+nS2q7p1srN+vtktm5vIkcWiiPcQZlUwLsw81Dzv/Gq/OrjYrUjKHj5yxGceYvT84ljF5nuyWenhA5+u4/PqkvH9bg7mKg/oaC9zwHPqeRziS8YEX9DXmJzC724kN7tLFLnEqudnaG6e01VOKjnyDX+ot+df8y6HVY4cQ7VPvjubrn/PXPaFPWu4slnhXcnnHvmUndzj2XN8JAdV3bA14/lmlrlbNjcVNA9FPnOIMIxOrrO/G7uDAoF2xJbf6vCiX5H0qM9KjgN3a7ySz0ag3OBjZ09x7HLR5Xqly2Gu/EsvMSOvPGhfP+63i9Nljs7Jze4Ckc+qgVZxg7+KV7i6/bNxEUPnTz4VX4U/81RhSLxHbWG7ssmexiqHxFTVRfaq8+g2j8xlW3Zu5XyFV/7AnHxOLOQzeY0c98otMXaYsDnjNQ1u2dyqJFPs6nCyd4aE+FodLu1x6DXPw4T/6gBAwoqkR31yINwvdneHhPgYO5/40D6yOWrvlsOU+sJPHm/dq/xyWPXPp4Xfba58udyRObnx/Fd62hdOckiNKl6y19UPTmELf3rudJCpRmJIey67w4RshSHx4m+XM2xm7lhnpNbCyFrngziU9+rcob8bwVSd65Wu8lPxVTrsdfvYJZ8Vfo/vaH5X9vA54zdsbiqKSCDCrA5vVzzIUhFJOhwibONL/vhhL310trt19N0n8yQyh6/zjS0fJVtdjvjAFs/Ep/HWQ+5+NeeA4cP3ldPOPnpZH+Lv9Ko6KY604ziqObnI/Feyis1zJp0uNuJKedllL3Ol56p+FRZfIwb3xTx9VHnznFUYKrySw4ePXb1S3uWqHBJTVRdsVXuel27O+XTcPicfYPA9x532ka9qSA7dls+JRaOv+/zMy2NinOf7mtzNn9wm4fcl/LvkT5dOdwCvxKjLp/LDxSAcV/obW3/lZ9dcuNxpDpO3v+btEfmgUU/OH59r1W+am32H5xGE/q42eTtdvd3ei53DXPngcp3m9tiDrot09elkLtrH5t/P0Ge9ULrPd55Pc3vT5ibS02AeecHJdn5yo+nl+jsfxEfF3n1yU130azR+xfYo/2P3782T31RMvj/vZWKa24XNjU9D/rv3al59kvmqS0CHrXqzvxIPF6nn4jvl4MpYv6MtGpzn/9E1/455+CpMvMzNbyk+r7Gp1tPcLmxuX3V4xu/nHprJ9+R7OPD9OTDNbZrb/IOO4cBwYDjwchyY5jakfjlSz1v193+rnhpNjR7NgWlu09ymuQ0HhgPDgZfjwDS3IfXLkfrRb4Rjfz51DAe+PwemuU1zm+Y2HBgODAdejgPT3N6c1J/xVYBnfsvl6x3zz7j//qaur3XM1zhu+9QyXwW4LV9X3RfT3N64ufEl7ne+uMlB9+Xad2tuu+a127/qYno1O+KXvmfY8ezV4v0O8WybG0XxL4Bq/hlfAuXLpytf+QVhPZPYDjuxVH8hY+WTixB9xjPNQTpVXPjobBLvvW/PXNqeL/LGSP6qPCHzmSO5Ie+Mqxh2+LDZXTrkqavHzn7u4+8qe2n/3mflcsWt3f69/jt9+aXeGrPm1Mll7uVt+qzOK5/K3G+XP9X8Xkxdfmb9Hz8dHmpuX1EQSPPz58+PJpCXD/tJOMlVFwfyeSicFMh0PrmYHIt8idiVT7edc8kndsngo7Invxyi7gCln+658+/yytXvv//+cdlVeFz2M+bkxvPPWpXLI5jQd5uux6V5Vfz4u8qeY71irpqvuLXbvwJD2pBP/bBODn2NPR+1f+bu4h7wPLDmPIMbjoM11wUTNqo9ZGb8xyZ1NifftrmJwCKSRpHHCaRguei7SykTArHSjsvtfHKo3OeKzG47511zwUdefo5fMdxzQMCcPhwjMopVculvlX/h80sA7DRmH1cYHI/m5Mbzr3WwuK3Kp+8Lo+PIOT7Ig3T1g5zHlzhXz8TgWDp59ye/qaNn1eWXX375yDfYUk72u3i1Dib0c/TaS17Pv/7660fjQJZ8ZSzE0O2n/NFn4djVgLhu9d3pyY43y3wGu2LusElHObsVE7ZnPN78vm1z4+DqkhIRkiyQpDrIFQG47HQoqn2t7XxWpOfyW9mt/HUHAB8Zl8tzwSimyvZuTbnzQ1rJe86FSfnXiGwXN+vgJ+9+QWrvzAEnN8IGDo2s41Nr+vTteDu+oJs2sU88wksMxHRrzTus+PJRtp3z4PQYyaPXkjg9nrSFjNvC945b2lcu3KfsOFZskSfJS4/1K8aMqbJJzjwXlVyuoZf5yTjJY9pf5RA+XZ2PjGGeD/xtSQoogvJTEfnKZHIoIBdkcxIhkwetw4F8Ryr2Vz4rHLInDI6tw+DreVDYwwc4tM4aPlaHBzur8Yi+ZPQjOxxIx6R17ScXhNEvvsTu9rC/wup7lS3ty+euBtSXBoXdzib7xJ56Xf3Q60b8ZS5dHhnqzV761HPGDV7s57NsdbnQnmqSseKffa+v1jq82qswur0z8xV+7B2RQbYawQ1Hec6aaF81IN96zvyk/V2OU36ej39a81xtP7m5sOaQZlfA1LvlWYdFl6ZG9wnR3BYXmwjmJHOZnQ3tH/HJIcaXxrzc02/3zGFxWz7nsEg/D0M+dz6qdepX5RJ5LkQ/yJVP8rGSoz4ug32PEd+rsfLH2ioebB6NAXmNHVZhP1N78K5i72wrh37uKrnEW/lbcaDKkeej2seH19h1rp4rbp2VzCFxcY7O1MexEpfsed5dRnM4LrkjPqu6pc15PtfQPG83NzcpU/Qklxu+Z14VX2srgjmxqzdP9rtL8IhP4uYQS6c6ZEdir/xVuc0LTTLVBXPEp2R2eZBM5ZMDTOyVLS7WSsZrsqtlFwv55/JidH/odrKOQ7LIVTa0T0zCjG2NXf1cpprjL+25rOpLbDn6GagwVHhlzy9dxSq7Vcw7blX7xFTZ87iumCtmYReOnT3iXOW6s4EfdOWv8su6fHG2JIdeZV97Xo9KZta+qLlxgI4Q7NYiOUFEkvxZkUa+tC+dPGjYrTCzl754xmceYvTOELUjOD60T57xTy4VQ17S7O1GMFd5QFd7xJ5j6nkcynnmghjcjl/Q+Dwykpusbeoil1j1nHlDtrMJ/qyBx53+V8/4S3uuc9R2JZd4qbfnX/Mu3ipHjq3aJ6bOpuvfM5d9Yc8armxWeFfy2sNP1kjPnrt8xq58rjhe1Q3dGe9vauTw1Cc3il+RWYUVAZIYONyN3UHhkO6I3REOfeFLDEd9VnLk4tZ4O4LjQ/vYVj67n10+MlY9rw58Xo6uL72ueQmr9jO/XZxu9+ic3FS8cxvyWV0uVdyreGWz2z8bFzFI3zH7XPFV+F1G8wpD4j1qC9uVTfY0VjkkpqousucNwW3dMpdt2bmV7xVe+QVz8ll7HWYwaF9ysl3VqdMn3g4T+zNe0+Bubm6QQgXKInCwzpAQWyJGRTjtaw8yaZ6HCf/VAVg1t6M+id39YrfDTFw5dj7xof3U4fnewyH85BGbjLu96qICzx9//PFxaWBL48qeyx2ZkxvPf6WnfeEkh9So4iV7Xf3gFLbw19WP/W4khrTn8jtMyFYYEi/+djnDZuaOdUZqLYysdT6IQ3mv7gv0dyOYqnO90lV+Kr5Kh71qn3jcH7H4uQGXx0b+d3xynVUMs3e+0W2bm5NARKjI4AVQ0SQjPV8/ModAXeEhHbbxBa6V3852tw5e98k8LwpIDi50V6NkqwOAj5Utxe0Hb+Wn2uMAVj5WttHL+hB/h6mqk2qVdiqsvkZuMv8uw1yxOS+k08VGXCkvW+xlrvRc1Q//3UgM7ot5+qjy5jmrMFR4JYcPH7t6pbzLVTkkpqou2Kr2uhz5OufTcfucfIDB9xy329Qc+a6G7Lu9SlZxuYzmK7+S9waZuOb5fDPL3G2bWyrM83XJ/8pc6tL5jEOmy6fyw6UgHF+Zh1f33TUXLm+aw6vn4TvER6OenH/OHTrN7U3/cDJv+Ku3zHsvBA5z5YPLdZrbYw+6LtLqEwf1n4v2sfn3M/RZL5Tu853n09zetLmJ9DSYR15wsp2f3Gh6uf7OB/FRsXef3FQX/Qrt7K8LH4X3Ve3ym4rJ9+e9TExzu7C58Tacv4PP5+qTzFcdah226s3+SjxcpJ6H75SDK2P9jrZocJ7/R9f8O+bhqzDxMje/pfi8xqZaT3O7sLl91eEZv597aCbfk+/hwPfnwDS3aW7zDzqGA8OB4cDLcWCa25D65Ug9b9Xf/616ajQ1ejQHprlNc5vmNhwYDgwHXo4D09yG1C9H6ke/EY79+dQxHPj+HJjmNs1tmttwYDgwHHg5DkxzG1K/HKnnrfr7v1VPjaZGj+bANLcnbG76vsx8T6y/HPhy+nxhtv/bmI++WJ7dvjik7wJqfPZY3hX/NLcna27zlw7q/9WLH+B3am784YDuC8K7fc/bzP/6wqQ/PjBfdv9rTp6JI4ebG4eEv3LwqKLzbX78MFb+qr98Ifn8VMNlh62zf/ZJ/tK2il01nPyrEJXerUQhju4ikz38Vvm61d8V8uSG3DOuYtj5le4qPvJ01Sc3+TvLmV0s9+5zLrt87vbv9b/TFy5qrjFxUquVzM5Htc/dUJ27oz65iyoblc9Z+16N8FBzg6BXXRYrEkAokRM51vJC65oNehq5XP1QyZ50dfBddjfv/OGD/MiXHwguGF/b+ar2O//IkqefP39+XP7gYf8rRmHIxkC+zuZD+U0ueGxcXlfFL38Zg/v7yjnccn47nt2+y145x++qxvDA68RaF88RjNhQw0z/7B31CZfuwXME88hc3xi3zY3iOhkeWQguaF3k7kf+84I5etknwd3uLfPOX3Vg0u69F+SROkhGl75GYc0c6rlqClxELo8/f6PWPGuQceZzVTfJKB+y57xKn+4LjImHZ48LO7KtmJA5y4OjtYO7+HP85EV49ANGZD0Pkk1byGkUHvLn6z7XvuyQt9TxfIGNUfgq7OwfGWVjl+9Khri1d8RPyrh+Zb9ac520p2fprPJV6cza9c3q1pxum1tFhlud3CLfEa26JHfYsHUVMTt/wqaLJS8oj1uXyz0XhvR3cUiGC0VYUr7DqXXHxsUre4rhnjymbXKSWHQJK7/yhYyeHRfru1yAXzWRDen5JY+do6P8VThcH/v4016lp33h8tqkHPmmltiqOIZf2XA8zNmXLvaw71gr+c4mst1I/lXjTkbr8u950Bp4z/qWHjZln5jBccZnchVbM359A1vVYNnc/BCIFDog/Jwl3wqM9twnshBeGFjTWJHX9zWHmMKd+im7e+784WN1mKXLodv5yf0qJ50MdakumKN59AsCP0diRNZH6VWNQT6qddclBmJir8LHnkb0st5d/Vy3mh/BWmGq6iYMGTd44U8+C1NXO9YzR8TBfl7yFV50KozsHRmp+W+//fYRK3dG8h9s5IPnxHrEp2Qyb1W98XGLT3S6HB/FN3Kf2wyXzY2iipwcPBVIc609othcCBwIxorwIi/7PiautJmH7CjpOn/49hy5TfIlfV8/OqcOGZfr62ArLo1aJ+b0KRsef2VbOi4je4qBC8H97uaVHvlYxSO7FTatZwyJIS859hVXxSP2u1H+VrF3uZa99JnPkkm85EcjmLpcdOs7vV0O0T8zyrbOhOeaHCWvZF854QxpfsYndtxnlWts3+IT7Pdgw++Mn9fgDjW3qqgr4txTwI5I8pcXzBkMXBw6TH55HMHc+cNmZY89P3RHfLnM7gKTbHVZVZdydZHmhYOM9GWbmpyJgfi5vDRmHYmVS9FlNQeHyyVm9jSCP+vR1c91q3mVR5ejPombZ89bhSHxVvnuMOA7cwS+bl/yqxyif2bssGacYAMH+x0/VlhU69Srcn3GJ/WQvRWG2fu8xnUk18vmtipqRZwjDncynU9I6QQ7iwFbfunscGm/88cFnpcph5XDe8RHJQPe7gIjZ1ymOboesuRRI3N8E4/buTVXbisvHfZ8FEb58xx2cUt2lVPy7rbkq6uf46jm8reKIXNa2WCtwpB4idvz3/lH1muML43d/i6HbuPWufJe4fU4yVnWEby38A2dzEHm+qxP9PKc3JqXkf/c5rdsbipGEkRrq2JLXocyiXa0sJ3tisAVtiN+sHXLAepyoXWagV+mHOQ8vEfwpUyXE+Tw5f61h17GKTnhkp5G10PnqoMs29VFB/YVTuqUXNrZ7PJxli/yv4vhqO1KLvHK31He7OrV5XDlQxh38Xr9cp7xsO91A1dyk3iq+KWvuyV1WPeXgZxL5//+3//7kdfUX/kUdrAmD4lrxs9tWkfzvW1uENULq3lFfkhQEfAoIIimA+Y61YGrLgrXER7JyKavC78w6lD4+m7e+eNwYY+cVQd056PbF+bO3m4va0Wduni69Q7bal05Sf+VvHy6HDlUnRSf67AnHV9nzj71YP1sXPLv2LDnIz47TMhWGNAF79Gcuc0OH7XOHHacQb7KO/6OjIrT+Ypdz4/meQ4Vu9ZcDn/Id7Eixyj5bGTYINeSXfn0fdfBx4zfs7GpLtvmJiEOn0inHydtFhfy5GFKue6Z5oYvxiSp9Cvypt3EvsOf+v7c+eNwQH5yAHYfqzjcRzcnDnwgR77kkzUf0ct6gDHXpctF5LiZp3/3Vc0lf+QyIg78iGPCrrHCKLvIanROEnNi7epX4fY1+XdfzDOuLm+Oo8JQ4aU++GLUumPTPHMnWXIGJp7R1bPnjHWN8pGx+f7RecaQGPBFbIyVnGSp+dEzJP+VbOLyfFWxdXYq2Vn7Ps3uUHObgn2PgumQdRfSVTXiMuwuhSsuvauwvqod1bnKM5d7d/m/aj6+Mq7qxeMr8Yzv43fxNLcn+sPJHDRdfo8iOT6qC1Rr1aX7KCzvaJdPYdXLxao275irR8e8qsWjfY/9402sy9U0tydqbirio9/eu09uXKzVpduRa9bPHdDqkxsX7bxcnMvpGS5+xm9KzuAanWMcePvmxqXN7/u78ZGflm4lqz5BPbLJ0OAyF9WnuVuxj/yxgym+Zf4fWfOpy1/rontB/wlA4+Tmr7l5lny8fXN7lkINzuc8YFO3qdtw4Gs4MM3tyX4tOQflaw7K5H3yPhx4Lg5Mc5vmNr92GQ4MB4YDL8eBaW5D6pcj9bxhP9cb9tRr6vUIDkxzm+Y2zW04MBwYDrwcB6a5DalfjtSPeAscm/PpYjjwXByY5jbNbZrbcGA4MBx4OQ5Mc3tCUj/6e27P/obKdxf9bzo+e0xn8fOdxfmO4m2fOuZ7brfl6yw/H6k3ze3Jmht/oeSdL25d1Ku/sflOzW3XvHb7j7xcnt32/IWS525wy+bGwci/lMDzI/5iAn9mCB+M1WVW/RUHyScuLjtsnf0TRvKXtnWAVw3Hc3jv2zNxrOxoT3FW+fqKy4bckHvGVQw7nNJdxUeernoBkL+znNnFcu8+/Oryudu/1/9OX7ioucbESa2Qqc7Xzgf7aaurWcpVuGSTu+geTGCb8fMb5bK5dQV55IGBUGok+GctL7Su2aCnkcvVD5XsSVdxuOxu3vnDR3WZSoeD6xh2vqr9zj+y5Onnz58fl3+FB9nPGoUhLxnydfbSUB6TCx4Pl9dV8ctfxuD+vnK+O4u7/Udhx++qxvDA6ySOr2rb4VXNpacRGdnKulU+WavOJ1yq9vAz4+c3riM5P9XcHnnYuaBFTA9ABEyiHr3sVwfMfezmnT8Oh0a3wcH47bffPg7ePQcEW+kj/XHAhTVzqOfq4uAicnn80ZgZswbuv5pXdZOcciGbHk/6dF9gBEeOHhd2ZFsxIXuWB0f5Dnfx5/jJjfDoB4zIeh4km7aQ0yg85M/Xfa592SFvqeP5Ahuj8FXY2T8yysYq347L7ZEX8PverfPKVoWLXGuv8qH1Vb4qnVn7+oZ3c3ODlB0R7i1qR7TqkqyI6v6xdRUxO3/CpovFLyh8S4ec3XNgpbuLQzJcKMKS8hVO5UvrfpnlpUAsac9z3c3TNnKJRTlSruQLGT07LtZ3uQC/aiIb0runBvJX4QCP28ef1io97QuX5zLlyDe1xFZyzP3Khp7zh7iliz3sO1b0XL6ziWw3kn/V+FaZFbbOVrcODo9DMXvupUvMLuc2k6u+N/N/5Nx3ycnNzU0E2B30e4KryA358jDqmQPb+YSYftF1srv1zh8+/DArTxwi8HeHZ+e3yknqIIMPDrZjAscuj44dP1WM7K1G6VV8kY9q3W0RAzGxV+FjTyN6uzhdZzU/grXCRE0ch+YZN3ipVT4LW1c71jNHxMN+npMKLzoVRvaOjNRcv7FQrDp7+uE8yAa4Ejc5S7xH/KZMxVn8UgOeV/6QSazpb56/V6O7qblRZD+sVxcUcnMgGCvyCQf7PiYJ06Yfslvwd/7wzeVEnsCRz7f4lOwRfV2IikujdIg5ayVMHn9lWzouI3tcWNg/GkOlx6VDfjpbFTbJZgypXzUHySiuikepn8/yx2WYe3ruYeZT2AAAIABJREFUcq299JnPkkm85Ecj/rpcdOs7vV0O0T8zyrbOhOeaHDmvlIvMa6V7BgN5cX9uR745t5r7Xs7BvpNLvXn+2mZ3U3PbHfIritkRqToIWvMDdMQ/F4eI7ZfHEd3OHzaxl3IcNOXviJ+UOaIv23mQq3pVF2nqIQNeanJrrhUHueEi0ZgXGvHKn8sxB4fLJWb2NIKferCXdWF9N1Z5dB3qA94cPW8VhsRb5bvDgO/MEfi6fcmvcoj+mbHDmnHKtvLh+frx48fHmdb6Gd/SIeaKZ+wRO5gqWfxTj3swYWvGz2t4h5sbpHh0gTsiVf6FxS+Oo8TB1q26nT8ucI36yYOCv+4C2uHe6ZMzvyR87n6RpY4amYODeNzGrblyW5kP9nwURvmTb9a7uCXL5YSsj1xYbkv7Xf1ct5rL3yqGzGllg7UKQ+Ilbs9/5x9ZrzG+NHb7uxy6jVvn1RmQjYyzstvhrWSrNWqRXJIse8kdfHYcRy/PSeV/1j6vee1yfbi57Q44jkQAEas7bMh1Y0ckCOh2q4uis+vr2OrI7LI+7/zRDDQSv19MOfcY3H4373KCfHdpoJdxCqcOuPQ06hlb6CgO1u4ZZbu7mLGLz8RJnTJfO5tdPrr6gaMb5X8Xw1HblVzilb+8gDts5K6rV5fDlQ/Z2sXb4dF6xoPsrm6Sk0wXu/Z0lpIn2CcXkpEs64zkIvXR6/yilzzE7ozfp6F5LQ41N4rbHSAMIrciILLdCNHSV3XgtJZEdbvCIxnZ9HWRtDsALpfzzh+HrjpQskFe7jkcq8tot5cXFXi6eLr1zMeRZ+Uk/Vd68ulyXJCqU+aNPelUttjPepyNS/4d28pnhwmdCkPiPZozt9nho9aZw44zyFd5x9+RUXF6s8DuKj/a6+KQT+0LVyXDvbE719hwbmguvQ4b+65zJAcj87VN71Bz00HYkYZCQp48TOzvRiepfPJTNTH5qtbdBxcHdjT6oXPZ3bzztyM/B/tsToSLOPKAka/uYKKXvld1Aq/njHn63+VM8tVllHrEgR/VSNg1JnbpknOXF+5Vrrr6JZZ8ln/8+JhxdXnznFUYqFHKuS/mVZ0zd5IlZ2Dimdj03J0D+cjY0LtllB1wOyZsZF6r2JDVSM2rM8+e+2OesSSuCpv7lXzl02Vm/rWNrMr/oeZWKc7a5xdTh6y7kK6qB5dhdZjlPy+Kq/yOnT/51OWZCzwb1eTuz9xdnYvqxeNqH2PvMfWb5lZ88fW7ko2DpsvvURjxUV2gWpvm9piDSD35FFa9XKxqg/6M19VnVYvJ83V5flQup7k9UXMTCR799t59cuNirS7dR5HzXe1Wn9y4aOfl4vMuVdXh0b8peVeOf0bcb9/cuLT5/Xw3PvLT0q2F1ieoRzYZGlzmovo0dyv2kT92OYtvmf9H1nzq8te66F5QY9M4uflrbp4lH2/f3J6lUIPzOQ/Y1G3qNhz4Gg5Mc3uyX0vOQfmagzJ5n7wPB56LA9PcprnNr12GA8OB4cDLcWCa25D65Ug9b9jP9YY99Zp6PYID09ymuU1zGw4MB4YDL8eBaW5D6pcj9SPeAsfmfLoYDjwXB6a5TXOb5jYcGA4MB16OA9PcnpDUj/6e27O/ofLdRX3h/dljuRc/31mc7yg+5lOHODZf9H5Mbu/l/jS3J2tu/IWSd764dVGvLpR3am675rXbv/cCeXd9/nLMfMH++zW4Q82Ny8L/YsKj3gQhi/vSvLrMqr/iINkkWuI/+yeM5C9t63B3DQe/Z/3lxYG9Ve611+Ur7X3GM7nJeq5i2OGSbsUH9MjTVS8A8ndVDcF41bhrXrv9q3B0djijGisZ8MGPKs9wGhmNnb3KR66lvepMuw7yHeeI4R5M7m/m1zTKbXPjcvKLgjUV/epC0NycKKwluSSzI2aFVfakK1Legr/zhw9yBF5h+/Hjx2UXY+efGPD78+fPj8sfPOx/xSgMeWGRr13tOrziXXLBZae5/Xk5cPE+4qx6znNOjX/77bePWom7KUOdfE/z5MsRvZTpnpUH5x358TXXBaMa6opzxKvR9Wf+Jxc/Oxfb5lZdqFyiTsqrgHe2RZokfYXNcWCrI67LHpl3/pLYkuMy0Zi4j/hKGQ7Z6vBIRgdQozDox+3ouTqgHHCXx5+/LWt+ayxV3YRJeZE9jyd9ui8wJh6ePS7syLZiQuYsD47WEL7hz/FTB+HRDxiR9TxINm0hp1F4yJ+v+1z7skPeUsfzBTZG4auws78bFdsff/zx4Rv/spl6WsuaEHcl7/qVru/fMlduunjxo5fUVc7AnfHcgmNkr22Eh5pbFhXCcoCuLAokSXJXlyTEk06FAVuJv5I9stb5EzZdLHlByebq4BzxiYzs7OKQDIdLWFK+w6l1P9xcvNT3njymbeJJLOKU8uu11LPjQneXC/CrJrIhvXs4K38VDvC4ffxprdLTvnB5bVKOfFNLbFUc28XFvnSxh33HSiwuL1ysnx2xl75YTx/wwvNT+ZY94qn2b1nL/KPr3JXMDlNnB3szXtu8dvncNjdIyOHm+SpiJcDq4OEzD8gRgnNY/KJLn0efO3/40Ji2riB8lZP0g4z8aY8L3jEdzWN1kFcxJhZ/lh7c8fUjeSEGYkK/wseeRvTO8MXtMD+CtcJETRyH5pkP8FKrfBaOrnasZ47Azn6e1wovOhVG9m4d8e85kI0qRjDpV5mZI/d7lotuw+fClo0L3OQVbFp3XZ9XMfn+zL9Zc6MgIoAaxBVNApvVyIWAL8Y8nNJ1TMhphJDYT5tJZOR2Y+cP31xObkdYVgfVZbt5HrRKTgdLcWnUPjELs8vnIa1sSydz1DUpt13NKz0up6xT6lfYJJMxpF53ySiuikepn8+7Gna5lp30mc+SSbzkRyNYulx06zu9XQ7Rv3cEn+J2Wx5z5m/FGc7ajjvuazUn14kv85PPlU1ivQpb5WPWjjfIw5/cuOwg5b0XdlekJDpyIl/6rC4K5LsRMuuQ+OXRyft65w+blT0RPXG7zSPzI4emOnyVb+oHVo3UFizIcEipyZnGQG64lDR2+ZA/l2MODvDpOTGzpxH8xMheVz/2u1H+OszSoT7gzdHzVmFIvFW+Owz4zhwRS7e/yyH69474V9xui5j5ByeOX3Vb5Zv8rDjgvro53PT6SBZszp8j+SJWj6XzPevHm9TZXC2bW0ciipikOAvC9fCZhwGfvl5dFG6rm2PrVvydPw6JHwZ8i+irg4rcagRvd2jIWV6qPLsesuRRI3MwEA/6Gm/Nlds6Er8wyo/nsItbsquLrbqchKerH1i7Uf5WMWROOzsdhsRL3J7/zj+yXmP33+3vcug27pnjPznGetZcvo5gy5zdihH95FFXyyOYiKmrxa0YR/6+BrhsbhQrLzYIkMRQMURiEfZsgbHdHQa3e/ay6uLakanzRzPwixlbwttdTMjsxi4n6HFQ0z96WT/JqXbS0+h66GT+8XXrKNu7+PGZOKmT11z+dza7fHT128V0pIZHbVdyiVf+qrNV4SR3Xb26HK58yNauZhWWag3/Fb4qF7t48JE5Yx39qmkig26VY/b8xSLnlZ5so+vnCZ8z3teozuRv2dxkUARMoqh4WkvCQmTt5UV1FBzkTNt6zgOntZUf4ZGMbLp/HeyMyfe7eeePfFSkPnIxdv58fXUZ7fYyb9Spi6dbdzxH58pJ+q905dPluChUJ8XnOuxJx9eZs5/1OBvXkRris8MEtgoDuuA9mjO36bljXSO1zhx2nEG+yrvbPTrHXpUX4nZskuuaBz6xWZ19bAr/yufOB74Yu3yxr1EyXR1cbuaf0+i2zU2FEElEFv9xQnqxkO32Xbaa09zcl+YVkeWrWne7TnZs3kps7HX+dBnJNpeTYsdXjju8+MqROPDBPvkSNtZ8RC/rsaoTl0di9xjdx2p+9KImDnyqRsKuMbHLHzl3eeHWHjFnrrr6rfBrr6tnXmRd3hxHhaHCS32Ij1HriTdzJ1lyBiae0dVzdw7kI2ND78iITzDn6PkgdmQqTFUu3IZj8lxUMpUtfK/O5ipf8o/fqj6Ob+af09iU50PNbQryeQVZ5VoHpzr8K51b97iYqoMu//dcerdieVf5Ls+6rHURZ6N61zx9p7hVmzkb3+OehBfT3J7oDyfzlvvIt0N8VBeo1uYAP/YA8wmgerlY1YYDPeNj61PllxfCR57Lyu+srWs9ze2JmpvI/Oi3dw5qXq5crLk+B2x9wM7kp/rkRtObl4vr832mRuhQlzkX36suqs/bNzcubX7v3o3f6a1Mn6AeeZhocJmL6tMch3zGaw+3+Jb5f2TNp37n6qeXzUf/p4KpzbnavH1zG+KcI87kbfI2HBgOfGcOTHN7sl9LfmcyDba57IYDw4HvwoFpbtPc/uGfln8Xcg6OuSiHA8OBsxyY5jbNbZrbcGA4MBx4OQ5McxtSvxypz77pjd58ShgOvA4HprlNc5vmNhwYDgwHXo4D09yekNSP/irAs7+98vUO/TPtZ4/lXvx8rWO+xvGYTyTzVYDH5PVe3kt/mtuTNTe+xP3OF7cu6tV3i96pue2a127/ikvknW3Ml7ifvLlxWfCl0kd+mRSy4IuxusyqL7pKPvEl/rN/5UH+0rYOdjYcnsFeYTpzIRDH6i1ce/JX5euMz3t1qlwI3yqGnc/Pbm7yd5Yzu1ju3d81r93+vf53+pxRjZUs+DgruzxzBiR/7wue+674CHawdWcKO12MVdyz9vimuP3kxuXkRFIRu0LfWzSamxOFtfQpmarZOAbwO3llT7oipcvu5p0/fHiO3Bbk32F1nWre+UeWPP38+fOjPh0e5D9jFIa8sMjX2XxMc/vzYoBbzm+v627fZa+cU2P+T9vibtqnUfme5skX9OA3zeZefssXtjx/+HF+spZ3ENiI915M2JvxT46fzcWyuXUHA1I6Ic4CSD1I5ISXjEiTpJeME7CztZJJndVz5+8IsXcX8sqv9sj56vBIRodPo7BmDvVcHU7q7PL44/AzZg12uKu6SUf5kE2PJ326LzCCI0ePCzuyrZiQPcsDYXUsXcxwF3+VjvDoB4zIeh5kP20hp1F4yJ+v+1z7skPeUsfzlfEIX4U95bpnxfbHH398+Ma/bKa81rImxF3JwyU1TOHLnKX91TP5p/mSL+mwl/bxr/20De6MJ+Xm+f6mdTSHy+bWFZlCVgQ86riT62xXxKoOh9vF1uogu/xu3vkTNl0seRjcng7PPTiO6EuGwyUs6a/DqXW/zKg7B/6ePKZtcpJYdAkqv/KFjJ4dF+u7XIBfNZEN6XHJEhO2jozSqXC4Lvbxp71KT/vC5bVJOfJNLbFVcQy/XVzsSxd72HesxOLynU1kj4zYS1+spw944fmRH5envpI9giFlPH63ixz2E5ueExc6GrW/44nLz/yxjW7Z3KrCqyCQg8NyZZGw7YcBHL4mn3reYeCw+EV3Fm/nDx/dYesOy1EcVU5SFxkOJD4d09E8Vod4F2Pi4Vl61YE/chEQAzFhs8LHnkb0zvDF7TA/grXCRE0ch+aZD/BSq3wWjq52rGeOwM5+npMKLzoVRvZuHfHvOZCNKkYw8clMMviTPjFUusgdGfEjbODL/OnZ7wyeqVHl515clc1ZO98Al81Nia2ITqEh25UF4EIQsfyn8iVsLsM8iZo2V29fq1g6f/h14kN09qS7sr3a6w6g68if4tKodWJOv8qNx1/Zlo7LyF7XpBxDNa/0tKa8ZJ1Sv8ImmYwh9ci910MyiqviUerns/xlQ3KZLteVzwpD4iU/jr/LRbcOvm5/l0P07x3xnzz0mDN/itvz7bLCk8+3YAQP3Mtnt4UfcdXxuIzPV7ZcbubnG9Ytuds2NxkTMbmkNf748ePjkkjC3uK4k02iIydfSTCt3XpZcXEoDr888LMaO3/YXNmr8K98+d6RQ1NdVtWlzIEFq8ZsZMhwAVCTW3OtGMiN8yfrSKzy53LMweFyiZk9jeAnRva6+rHfjVUeXZb6gDdHz1uFIfFW+e4w4DtzBL5uX/KrHKJ/74h/xe22iLn6b16qGxwhF66PbtbX7XfzzD/4Mn96Vh1Zl56eHUf66Gyl3Dx/o+aWxXhkESsyyz8+nVxJ1MTZPWPLL51O1tc7f1zgq8OGTw6L293Nd7rkLC9Vnt0nsuRRI3NwEA/6Gm/NldviomKtGrlMPIdd3JJdXczd5dfVr8Lja/K3iiFz6ro5rzAkXuL2/Hf+kfUau89uf5dDt3HPHP/JMdYVo9dcvhybz8GR+WJ9N8pP5hEcnj/472vgqvDit7LF3oyf09A8z4c+ubmC5ip+d7mIxCJAEiNtdM/dRVERp7ooOru+jq1bL+zOH4dBo/vxOT7P5KXLCfa7w45exkn9pKc6Om508jLC162jbOeFkjbwmTi7nO1sdvno6pd48lk128Vw1HYll3jlrztfiY3cdfXqcrjyIVu7eBNH94z/Cl+VC4+HuTf5al7xt2pC8lfp+5ryop9KX360rv0q3qxjJTNrn9fkbm5uK+JDZBEgL6qjRYXQeRgqv1pb+REeycim++/I6zLVvPMH6f2QuT4xHb2wXJe5MHf6u728qKhTF0+3DpZbRuUk/Vf68ulyXBTVZcKedCpb7Gc9zsal/Dq2lc8OEzoVhsR7NGdus8NHrRUD8ho7ziBf5d31j86xV+WFuB2b5Dqe4xO9rK/22RP+yic2GMHnGLDhdwtnuMuz7MnGah+fM35Og9s2NxVMROFnRxjt33MwIBH+GJ1okEO+qnX2NUJU7GjcHR7X93nnT4dMdjlsmTPt+eFxm0fnxIEP9MhXVxf00v+qThx4zxnz9A+ObpT8kQNPHPhRjYRdY2KXL9lFVqPXlJgTa1e/DjvrVT3lM+Pq8uY4KgwVXurjMWqudXAxZu4kR87AxDM6evacsa5RPjI239/N8ZnYefZ8EDt7HSb3iY7bYd9zUe0jxwjWzA8+wKVxhQ2/VX3wNePnNDXyvG1uCM74uYWp8q2Dszpglc6taxz26qXh3kvvVizvKt/lWZe1Ltm8iN81T98pbtXmnheC7xTLq2CZ5vZEfziZt8lHvh3io7pAtTYH+LEvOXwCqF4uVrV5lQvpGePghfCR5/IZ8/LVmKe5PVFzE1ke/fbOQc3LlYs117+awK/ov/rkRtObl4vHvlzcyifqMufie9VFdXz75sal7b9br+bf6a1Mn6AeeZhocJmH6tPcrZfByB+7BMS3zP8jaz51OVaXzJNeNh/9nwrS5zwfq9XbN7chyjGiTJ4mT8OB4cAzcWCa25P9WvKZyDVY5zIcDgwHvooD09ymuf3DPy3/KjKO37kIhwPDgas4MM1tmts0t+HAcGA48HIcmOY2pH45Ul/15jd25lPEcOB5OTDNbZrbNLfhwHBgOPByHJjmNqR+OVLP2/bzvm1P7aZ2V3Fgmts0t2luw4HhwHDg5TgwzW1I/XKkvurNb+zMp4jhwPNyYJrbNLdpbsOB4cBw4OU4MM1tSP1ypJ637ed9257aTe2u4sA0t2lu09yGA8OB4cDLcWCa25D65Uh91Zvf2JlPEcOB5+XANLdpbtPchgPDgeHAy3FgmtuQ+uVIPW/bz/u2PbWb2l3FgWlu09ymuQ0HhgPDgZfjwDS3IfXLkfqqN7+xM58ihgPPy4FpbtPcprkNB4YDw4GX48A0tyH1y5F63raf9217aje1u4oD09ymuU1zGw4MB4YDL8eBaW5D6pcj9VVvfmNnPkUMB56XA9PcprlNcxsODAeGAy/HgWluQ+qXI/W8bT/v2/bUbmp3FQemuU1zm+Y2HBgODAdejgPT3IbUL0fqq978xs58ihgOPC8HprlNc5vmNhwYDgwHXo4D09yG1C9H6nnbft637and1O4qDkxzm+Y2zW04MBwYDrwcB6a5DalfjtRXvfmNnfkUMRx4Xg5Mc5vmNs1tODAcGA68HAemuQ2pX47U87b9vG/bU7up3VUcePnm9q//+q9/+5//+Z+//e///u/Hz3/913/97Z//+Z+/1YX+n//5nx/Y/uM//uM0Ltn4jrFdRVTZUd0Uo2I9Yhd51f7f/u3fDukcsXuPzCvWSbnVGdNZuyc3o/uPje1Kvlxp6xlq9fLNzYvwXYsrXLqAV81th32373l41jnNSrEeiQH5aW7/eGkeyd9RmWluj8vvlef6SltHufGVck/f3PwC2116z1zcHfbd/iNIJp98Imb87//+77/9y7/8y6Hmcysmai2/t+p+F/nPrpNemFSb/FTPbzSu+ET7HZqbOCfuwUMfhy9/b76fzb2vPnNP39x0SEXqHz9+fIyri/WZi7vDvtt/BNHSJxfMoxrcNLfbPyGouelXhqqJN7JXbW7i5CO4/lU284zdg+NKW/fg+Czdp29uOrx6K/3ll1/+4QBnEnfF1eH3Nz7meVnLDnsa89eJ/ibrsjs7fvkIOxeQ+/K5v40T26+//vqX/8boNiWjH97mNXcfLpu5q57xqabDPrbdFk3JsWfO9Ox1RNblsCO/+KOhSh5Z5LDR/fcg2ckcSMex40dy2PPRsSC7GiWvOLs6EY/XFnvC1eFDJkflRPHr5c+xUveMNeMkp24XXc9DlWPwIuf+sUe8yFR2kF2N2Kl8oIdM+sh1noVf8YMtz6/sJtckmzkTJv1k3jL3suf+8JtcSJ8ZD/EesYXsK45P3dwoMmSCRF2htJ9EQZaDCOEguMtXaxBWttOWyMk6WN0e8tjAN+s+rrBLTvvy50RXXvxASkbPP3/+/LjAJfvHH398XLTCBVb3u5pXmOTTMUhf/hQjtsg1ddO65okfOfJCDsFJPTxGfDBKN/GwJzvy6foVfsm5DLgcPzZ3I7Zkj5ykz3zGJrqKm7XdiC1hVq3xmZwjl85PZOQXP8Su0dcyx/jFH/bdVrcmGdUa+0fGylalV8Ukf44fW+IG+YB7PGP7CLdl/wzP5EO67hNsWgdD5ho95yxrbgv9Vx2furmJqHlJZEG9cEmU3V6SRs+V/ZTjAtC6++j0OXB+Ybie5ivs7PsB1VralQ1kHGN3cBNDPicm/O0OUOVPudEF4DngIJNH9OSXeVUPxyl7xOzrmns+2CMGcCQGyeF7Fyc2fax84kN7kgUDcWsNGV9zu91c8sSvOfr4IE6tV7l0feIGJz4zxx3WlEsM2Dsz4jOxVbaEA675HFlsZX0TP/I+kiPXrWqeseczNqXrtqo64ZPYj9rCx6uOT93cVGgvfFdUipdEYR1yuC3tOZE6Gcml3+rA4KsaU7+S6bAjW+2nXZdxjKvYsF+NsqdLwn+Us0o21xyL9jzXyHLJYBOcv//++0fdq8sYXcbVhZQYpJM54xkMkgGH9PFzdKx8Yg/+5bNsr+JY+RZumpvyKR8aiUt2K3/YdDmfs19h67CmPvWl0bjNW+duy/moudcOu6oDcllHbKVe4sdWjlnjfJZ82pKvis+uS50Sr+y53BFbifkVnw81NyUOIjB2hWdfY1UsEd9lNOdQ35LgqtCsdfacAOkLXBq1B8EhErZ5dn2ISk7SlstWc/TxXcmssEu+2k+7LuMYia3LW4UnfZKvqubgWNW9OpDYJK/gxM4RvIqTyz3j8HywB1avheQ8Ls8dekfHyqd0cz1xa18/R/0gp9x5/LKhNY+TvFb2kUsd7GtMrJKlRtXoucU3co7VfezmcKWKodJF3uuKHHuKgzWN5MLxswZ+RuemMPlzZUu+KiyuCy585IiPI7Y8rt08a4Rfz4PHxL7GLiaX0TxzvcN0ZP9Qczti6LNlOlIpUd0BcaIkXiU3E+4HhQL7GjbAQrE1yhbPyHVj6ldyK+ySr/bTrss4RmLjcFT+qzW3p31sOlHBIFm3kbrVgeQwYw+c0sXuDrMw3cIH7FI7fCY32PeYjswzbungw3PksTM/41O58/gVnz758g9aZLPyTyyeD5+zr1E23Ec+u+xqjn23tZL3PXLkOfR9nxOv/hukfpJD2IJ36IKPOvCcPrPG+Sx76GKr4r/kXBfc6Q98jEdsIfvK49M2t66AkCaJqSI6UbyoHZldRvPOZ66LsFc3t/SR2KrYyAUHyGUcI4cmD3n6yGe3pz3s+NuacFeXVepW8WVdsC9d+SMGnhMfMpV/7SUGrWXO5KPTr/zt1lY+lQPX17Nq8u///u/lG7DLdvPMv3Ko5vbbb799xAU3qvzLpq9nPbRPTTxHmcMOW7V+VhdsKy7gz3MCh7TGPrZ8TXueC549bvSzxvksuYyz4hkyfi4rW/hlPGoL+Vcdn7K5caAqIrPnhKB4HTHQqeyhqxHSuxwE9IPAgdHo+t0cGyt5bLoft1fFlnZdBnsaib/KmfvIudtjD7vgzGd8qfm7v7w4ZI98Ywtdz7/2ZAsZcDDKf3UBab/CnznLZ+yeHdMnMXkusI3vVXzIdqPykvErJ3oB0brm0iXXnlv8e2617y8vPGtN8uDQevplj1G+3bbWK7zIr8YKfyUvn5nPxIotx1blIm1Ry+S27Gd9sdflHwz5yRI92azi0xq6yPCctjr9V1l/yuZGgSFGFsMPiOYiW/VTkTfl8oBCFJdLHJA+1x1nZQebfnm4TsbiB+bIAXIZx8ihdHvut5u7PWSw5TEkbvlOXcm4juyRI+qEbeniT6OelTvW4Qf59NFjTAyyha7XLvFjz205ntWcvGNDI7hTj3iTgym3ehb21Cev8u1x+jr4fF9+wMS+7Ctn2dwkW+Utc5YyyYFVbL5XYQcj+aW26QNd8sQz+oyZiypGySSv8ll6YHGbrMkfWJSfzNkRfEdteQ5fbf6Uze3qIkAEDgH2Och5GNif8fa/mPFsOePy9UtIMXScuTI++JeX25U+xtY/cpjmodpPfv4xP8+Sk2lu9t9u8gJTEdXwprk9L8HvPYhd/bkA84XoXn+uTwOteOlyM7+Wn9R2mtu1ef1snk5zW7yF61LRrwgeeYF9dsHH320HtvvkJk6IG4/lEXOiAAAgAElEQVRqPFyww73b6nUFv8n9NLfPz/0V9cPGNLf/9z8r5S2Z368zPuryogAzfv8DRIODExof9WneeTiN7Wu4Mc3ta/J+9V04zW3+T9zz3xWGA8OB4cDLcWCa25D65Uh99Rvg2HuNN/mp43vVcZrbNLdpbsOB4cBw4OU4MM1tSP1ypJ439Pd6Q596T70rDkxzm+Y2zW04MBwYDrwcB6a5DalfjtTVW9yszdv9cOC9ODDNbZrbNLfhwHBgOPByHJjm9oSk1veu5k8y/fkWqu+DTT7+zMdVn1D4819Xfd9u6nRNjZTHq2pyFVe+o51pbk/W3PirKfPl8j8virk0/8zFlZfMNLfH5PXeGvFF//kLKuv6HG5uJJS/Vn1vgTp9DpT/NYjuL0LoUks5PedbPNiRPRtDd4lWDSf/qkVi6uJfrRPHitT4fdRf0Fjhq/aokUbfV87O1sHtaN7VJeUe+QwH4JiPz/oiwlnM2p3N46PrxPkg9x2/OCPI7c4m8mfOVGLCJ2PmVs/saex8wrdn5dZZDt2it21uEFwE+PHjx2UXUgcSf1501rLQRw4LJPCGIHvS1Z/Z6XBU650/fEA0+fIDw5/z8bXK/m6t848eefr58+fHoQAP+18xCrMuGf2/pHTQwSBs3eWDzNFxl5ejdu6RSw7cY+u76MIn5fcKTI+sk7il+8E5Bvd87dazKV3xdNVozuQGu5xRcu13BGt57+FP8XV7yLzzuG1uSiCNQeNVF1KXdAoqvy5TXYaScTK4vObYWsmkzuq583fkYrs3d3kYKpyS4YALa+ZQz9VhoPm6PP78LVLzW+uPTzVceCTsVT3Bgc/Ol+wgw1jVOOXcP/nLOKv8ILsaj3AAX+kj1/XsdVzFiC4ymTNyKnyej8RAbKoXthidF5LDJvudLfeHbFUn7FV74Dozkpuq7m5P+5k39hW7cOnFvosT2VtGzoVilx5YVSe3U50T9tHZxYf8u43b5uYJWZHA5e6Z05DyQFVFhnjSqXxi6ypSdv6ETYc3iemY7s2d9HdxSIYLQlhSvsOpdT/ceWjuySOHWD706Y3DnD7BphjIm+aZV+xhR7JVXVIuY5Jet6ZGDIajI/g1rnSQI84qt+BS7IpD9mgAPLOmZ+e/nr2W6LktfMIV2VqtuU+wgV+62k+udWvuU7r6ISeOm717xgprZU+xVL6Fi3XJZIyVrSNrFa5qTbZWfquaHfH/LjJP0dw4oH7IVCA9V4fFi8fB8cPt+7fMO3/40NjZqw57J5vrkDjjdzlkuHQ4LI7paB6rA3UkRsfD3OPWHDwauTjAnvGxTo2rmORHesjouZPLuBwDeM+Ot+RHOIjd5/gGf+Yj8SPvI7qS1To19/xoPW1VuSD/jiNz7T7wCQbZdGyVrusnRtc9Mz9aE+HKxkXeiCnzdQYPOpU/7cmH31M8Zx6xg05i9/13nn/b5qYi+09FfJHEZZhDSArLIWX/LBk6f9jtSMghkz6YbhnzoFW6ulAUl0btE3P6zENa2ZZO5kgxcCFX/rs1tyVsv//++wc2t8dlmHWTTcfrc/cnH86PTs59Sh+/Z+Jy/5pTY7jAWNmmNshk3OCSTfeT+H2PedYzn5HLHGUOJQdO7em5s5VyaRuflQ/2rh7BmjxOP9SNGNnPGPIZuVtHait7lS774kbFndQ5wonUeZfnb9vckmx6zmKfOSyQWeTR/JZCd/6wWdljzy/fW3xKloPaHQjJVIdPa5kzDg9YNeYFgAz+uLzOxKCcYR878qkfsOEPTJ4fj6GKUbJZFz3TOHLEJz7ILXJgZf/oKOy3cIqYq5yyl/nwnIFLOQG7j9SO+Hh2PY81cyg56qU9PYPL/fgcuaN1AsvVIzFnrdMPNcsaEKfnv4spbe6elSPPu8vLh/JJrSSrZ/LqsswrTrD37uPTNDcI64XWPIl5pKDYulW388ch8cMgHBySjsxHsEoGvJA+9biE/KLxueshSx41Mscu8biNW3OFLdn2+GVbaxq5fMhT5k82hB19n2Nfo+w5vk7Odao5ceOvkunW0K1iSB3qKczylfnv8iHb5Ew2Fadq5D6xrT3J5DNYMkeZQ8klVzpb2GRM26xXPti7agRz5iXtk+OsNfpZky6mtLt6xie1cVn4k3t6XsWSnHCb7z6/vLmJFCpGFuloojtyVQfr7GHBll+IR/B1/iCmXzIQOQ/PET8p0+UEOXy5f+2hl3FKTrikp9H10MnDja9bR9nxHCj3wvPbb7/9/xd15zPXhdMvd2Ehdo+xkjuK+6yu9FaXkPv3nFSXFzHJZuoRJ7nhGTm4zfnLZ+S073XJZ8kRE1zAJ8/YyrHKITElXumCsdpL26tn8O3qABaPH7vsyUb3k3pH/Xrd8cdY8UB71IB6Is9Y1Y29dx8vbW6QVKQ4S1SIkgdIz3mxaW3lR3gkI5te6I5ILlPNO38QUKP0OCB5CCqbR9dWJN7tZd6oUxdPt34Uq8vJVuZBePUvJx1X5lA2JOcyjlv7PMuW8wAOpV/HhX1qxl6Fl73VWOGv5BWTX74VVvjj2Cr7wur5QU/25Uf+yRHPYNKz5wdd5PSsff3ID3rgQI51H/GJHs9ZJ3Sw6bGwd3Qkj57bSpc4PfZKLtcyX76PTfkmZt/XHJkub+xXPO7yQsyuk37f+Xnb3FQMFa36qZKq4kq2K+Iu2RQs/XW+qnX3AWnc3q3Exp5iq/xxODVKlhy4T+aVPvZXI3HgA1nydeuhAmNVJy4jMPuY/sHRjfKT+SaWPLTkEX+pJx/oSgZ9xVDllRixpzHzlDKVnS42X0/s7pOcIZM+iIl4eXYbxOo+qT1y0peuRupKLXlGX8/4Yw18ssee8pM5O4LPZcDe1QmMmRdwHRkdO/lgxL/sZL2R0bjyX+ULXF4Has0eo/w6DtZ99JyBizq4HHPkO5/Iveu4bW7vmpjvGLcOyIrsV2BeXTRHDugVGN7dxlxa678Z+O78IH6dx1VDRu5dx2luT/SHk7n0ROpHERYf+aYvf1rbvX0+Ctc72aUG80Y+Ta7jPZ9UhyM9R6a5PVFzE9EhddV8uoNwy3r3yY0Ld94U+8N0S55XsuR6Lq7H53pVh++6Bz8edQd817hvxfX2zQ2i8Dvubnzkp6VbiyZSP7LJ0OAyF3OYPueyhZPT3D4n37eev6+W1130ne6jr85H5//tm1uXmFmfi2U4MBwYDjwvB6a5PdmvJeewPe9hm9pN7YYDn8eBaW7T3B72j1PmIH/eQZ5cT66HA3/lwDS3aW7T3IYDw4HhwMtxYJrbkPrlSD1vsH99g518TD7ekQPT3Ka5TXMbDgwHhgMvx4Fpbk9I6kd/FeDZ3vL0z6If+dWIZ8vHVXj5s1JX/bPzqdM1nyCVx6tqchVXvqOdaW5P1tz4Evd8B+rPi2IuzT9zceUlM83tMXm9t0Z8D3K+d7quz6HmpiT6F3of+ZbMgXJ/mld/U1GXWsrpOfFBBmTP/gmp7hJdNRz/QvS9ZCSOlR1qVeXr3kN1Rp8aaXR95exsHdyO5l1dUu6Rz3AAjvn4rC8inMWs3dk8PrpOnA9yv+NXdzY5Q9jJ8Z56OsbKTvrucg/fKhtn6/NqetvmpmR7s4AQvnZlUqoDxVpe2EcOCyRQHOCUPekqFtaOjJ0/fFREkw6HwzEc8ZcynX/kyNPPnz8/XgYqPMh+1ijMumT0vzvRwcavsO0uH2R34y4vO/0r9lccuML+V9iAT8rvFf4fWSdxS/eDcwzu+ZrHof1bzqbOb95Bbm83J5/4zPOZeIVbZ0TrlW2t34OnsvlKa9vmVgWrIl91MaV9CJAFrS5DyayaLLZWMul/9dz56y42yKn/MadIeE9zw1YeCMcrGQ64sGYO9VwdBl5YXB5/HETGW+uOTzVcj7+qJzh2vmQHGcaqxinn/slbxlnlB9nV2HHAdfCVPnJdz17HVYzoIpP1IafC5/lIDOBUvbDF6LyQHDbZ72y5P2SrOmGv2gPXmZHcrOp+9GyCMXNxCy44z/+oV8/og9XXtIeO9pFlRKeKD5l3Ht+iuXWH79bCi9jVARQBdXidmDRW6XAw7iGhdHdxSAZ8wpLyFU7lQOt+KeahIZa0dyR/il968qFPb8pF5RNsniPNM6/Yw45sVXVJuYxJet2aGvGR2FwG/Bp9PefIEWeVW3ApdsUhG3CIZ9b0LBv40bPXEj23hU+4It3VmvsEG/ilq/3kRrfmPsFMThw3e/eMFVbZI1ZhJD8eT+VT+/fgcz/gcq7IfuYQnKpdhY/9KqdVDO+2dqq5VcS9KnEUTD6wCTF8TXt63hWWg+OHG7u3jp0/fHRkBX9F0CMYqpykHjL4qA4QOHZ5rA5aFWNiqJ7li0OrOTnSyGUB9sTFOjWuYpJP6SGj504u43IMFfZb1m7Jj3AQu8/xB/7MR+JH3kd0Jat1au750XraqnJB/h1H5tp94BMMsunYKl3XT4yue2be1cRjJz9gr/wg43mo5FZrHnuVH9+XHXz++PHjg9udb49l5f8d925ubhCmS/a9SeRAqRn5T0V8YXAZ5knUtMlleyvWzh9+OcwQExz5fKvfI/o6MIpLo+wTc9YpD0NlWzqZI8XGhXwLfrclbL///vsHNrfHYSdfbt/x+txl5MP50cm5T+nj90xc7l9z2YYHPla2qQ1yGTe4ZNP9JH7fY571zGfkMkeZQ8mBU3t67mylXNrGZ+WDvatHsCaPWSfn+VzhkGxVx0q2Wst65rN0PDde58xt2nfZ3Hv355uamxKpA+kXydUJ7Iqp4ifBnBBHcRCD4tD8qJ7kOn/YxF7KHTlAKxxH9KsLpTqUebCEOS8AZLgAqMmZuisX2MeOfOqHeuKP/HkuPIYqxqou8knjyBGf+CC3yIGV/aOjsN/CKWKucspe5sNzBi7lBOw+Ujvi49n1PNbkrOSol/b0DC7343PkjtYJLFePxJy1lp+ME9nMD5jYJzbWj46ZQ+mRR68vuPRJzetS6bvvihO+/87zw82NgnjiH5G4rpgVySCEdG7Bgq3qYlnZ6fyJYDrkGiuy4a87QCuf2tvpkzO/aHzufpHlsGpkDg7icRu35gpbsu2ckW2teZ7gltbQY/SL0ufsa5Q9x9fJuU41J27HW8lVa+hWMaQ89RRm+cr8d/mQbb+wFSe8wwe2tae1fEYuc5Q5lFxypbOFTca0zXrlg72rRjBnXmQ/86e1XUyKxXN+K84qF1V9JSfMzuMj+KqYbsX4qvKHmhvFOHLoRWAVScU6kzTImQe+IuHZw4KtJNIOb+dPBOMwEb+eu59bc9PlBLzURzhY04hexik51VJ6Gl0Pncy/271lLjvOG+VeePgXY8LQ+cx14cyLhtg9xkruKOazutKDAztfnhMuNemjR0y+pj3pESe54RlduA3H8hk57Xtd8llyxAQX8MkztnKU3pE6oQfGjIX9oyP4ujoId3cmWSdv8gmuXbydX1/HfjUqX13Nq1x6Pqq6+f47z7fNjaT7QegSBhlUwLNEhRBJKD3ngdHayo/wSEY2HbMIIYwijq/v5p0/2VnZIy9+cHa+cn9F4t1e5g08XTzdemI68ixbyR3h1b+cdFxVDiXnMo5bvnmWLecBHEq/iVf2kwMV3tSrniv8lZx8OlcqrJw5x1bZF1bPD3qyLz/yT454BpOePT/oIqdn7etHftADB3Ks+4hP9HjOOqGDTY+FvaMjefTcHtEFWxWP1o5gInfyTcwr38h7fSUv3VVN0iYxO/dT5p2ft81NCVfRqp8qqchXZDmSaAqW/jpf1br7gUhuzwnksru5Yqv8cTiTrNhbHSBkdiNxpA/yJWyVDfSyHqs6gddzxjz9Vz59TX4y32DKi4M84iv1ZBddyaCv2Kq6ECP2NGaeUqay4/F088TuPskZMumDmIiXZ7dBrO6f2iMnfelqpN7Ukmf09Yw/1sAne+wpP5mzI/hcBuxdncCYeQHXkdGxkw9G/Fd28J35Yf0IJq8Dta58sUZuKtnkY+LChsaVHZd71/m2ub1rYr5j3CI+l86j8K0OtfyvLopHYXo3u3Nprf9m4LvxoYtX5/FI8+30X319mtsT/eFkLj2R+lHExEf1xqi1aW6Pv3ipQfVm/6i6j93H1/XKHPNJdTjS122a2xM1Nx0OSF01nysOT/fJjQt33hT7w3RF/mWDXM/F9fhcX1Wzz7QDPx51B3xmLI/09fbNDaLw+/lufOSnpVsLLFI/ssnQ4DIXc5g+57KFk9PcPifft56/r5bXXfSd7qOvzkfn/+2bW5eYWZ+LZTgwHBgOPC8Hprk92a8l57A972Gb2k3thgOfx4FpbtPcHvaPU+Ygf95BnlxProcDf+XANLdpbtPchgPDgeHAy3FgmtuQ+uVIPW+wf32DnXxMPt6RA9PcprlNcxsODAeGAy/HgWluQ+qXI/U7vqVOzPPpbDjwVw5Mc3vC5vbo77k92yHRd34e+b2/Z8vHVXj5m4lXfadq6vTXy/dsnZTHq2pyFsMz6E1ze7Lmxl8omS/4/nlRzKX5Zy6uvHSmuT0mr/fWiC/5zx9VWNdn29y4TP2vVTzyLZkD5f40r/5gsC61lNNz4oMMyJ79+4jdJUqOaDg846/CdIbgxLEitfbkr8rXGZ/36lAjjW5LOTpbB7ejeVeXlHvkc1Vz6g8vHun/EbY5i1m7s74+s07y1Z27/As8Ox7ee6bQhw8adzlFpzvH8O1ZuXWWQ7fobZtbGoMY2UBS7uxzdaBYy0IfOSyQQGQBk+xJV7GwdmTs/OGjI9pVOev8g508/fz586O5dXiQ/4xRmHV56P/lpeaMT2HbXSrI7sZdXnb6V+zvOHCFj8+2AZ+U3yt8f1adqEXV3HhB9Jg077iIvGzl/XM2J9h0DG6L/Z1P6V+Fyf2/yvzm5qbA1SgeldTuQFWXoYq7arLYWsncUsjOH4dJY2fv3pxB+JUPyaguGoVVP45Hz1XdaL4ujz8dMP/pLgH343N8quH6C0ZVT3Dgr/MlO8gwVjVOOfcPxoyzyg+yq/EIB/CVPnJdz17HVYzoIpM5I6fC5/lIDMSmemGL0XkhOWyy39lyf8hWdcJetQeuoyNnXpj1kzarNddJP8j/+PGjPDspf/QZu/KdOuztfFL7itdp8x2f36K5dYfv1oJDuiTkkYtNBLwHxxF9yXCYhSn9dTi17pdiHhoOf9o7kj/lTHryoU9vusiklz7B5gdVc12K2sMX9rCj9aouKZcxSa9bUyPG39ER/I610kWOOKvcgkuxKw7ZoQHwzJqenY969lqi57bwCVdka7XmPsEGfulqP7nRrblP6eqHnDhu9v6/9s7oOpJcSbKryUgzmjwVWo6nQf21AC3h7Lm9507bs3VERCYjWUwSHzwIAO7m5uaOQLKqyHp0hJdc4JDx1CK5Z3z9jAkvOSWu+x8Zm5tYj8ScaibOHv/rfx6+3KbmvlNIC0bxxbUpc429VYPox+jBycOd+488r+IZg3HC+6hmkyYdRxsPrjGT01Udp4N8lmPzcY5mvjR4lg+jLw65s68fo+u+oKacsOu6rOw6r+SQcZ95fkQfeJh7PhtX/q1H89c+R32xZd2aq6G2jTVpof7Jo7XOGMaUA5jGY5x80785pu+V547b8XofTHX497///b81SU7mpB16XuFyZLPqFWv1SMw7eR1xfse9S5ebTcEFccclcSSUB8pYjlPj07zu52hzGKcxfdm6f3VcxTN2HuY7Neumn/gSj7wY2TdnOKd9H4YJG5/WaHr5Je7qObHg9tdff/3NLfHUqusGZvLN54xHjOyPlV3GxN+4XjSJ+egz2PZBjhO2tdGu85YXmMmj+eeez13PnmvXGrWG2MmTPeYrrLZrbGNOMdy7Y2z8nqeuzbm17Rx6/ijf7g/wGqNj9LztmTfvyeanrl263FocmmY6tG33zLybTowpZjevtkdjNhnPR7a9t4on5hHexL/xV/PVSyXtp4PAWtcpDzj+cO6LTBv8sbEmeYFk7KNn8hZfHGLyJTfjTfplDlOOxO66MPfi6NGYclZb7eTq/tUR7mBMOUwY5jxp6l5jMW/+aCL3HK2d+TmXS2vZGmJnvdhjLq+Mk8/aNbYxpxjufXSctOl48ue7NOqcmqS/dqn/KqdneKtr9tqzMZP3M1y+s89Tl9vqwNwhlIX3oIhpzFzv5tX2bBRrerEc+a7i0WAc8jwMjWPMPFBts5qf+apZvmjyOWNqq46MPhvffBLjUa3EAjsPMdisMfqing62/vlSyWf3GcFLfiu79JmezTv5TnbTmr6M036uWU84E6v1X+mRmoFHnt13YrOHTc/l0Rq1hth1r6ywxHRsbNenGO59ZFzx6njatWbElvO//vWvv3upa+I+GB/hqm/WuHXW5krM7gl99/jE37khmk2C+C0iTUHzTHttO81XhZ5idvNOeNOaWPlCnOx6bRXvyovNmM/ostJEfnlQXGPUr/OELy9V/BiZ66dPH273Hx3BycsCHeCTf8exitnr00E298xxsrvK+1lf/KaX5hQ3NaEf2s+cwEz/7D+1ybyx7T7ruXjEzbr0HDtzsheM6VysHicNzan54ivHaa+xp7k80XH1JXZqKFbmJc8VDuupGxj6s9c1M0aPxsHe50diijfVzb2fPj78nZuF7AIjpE1KkWymRwUWvw8Qcz/pizk1qnvywQbMXJ9eKLm/el7F83CtGtucJs1WsXr9qInP9lo367TKZ7XenK7Mweq84cu/nExek4bYpU3yJrZzsLLfruoNftds4nslz4n/5EfMfAlOXH3ZJbcJH66pj37gEyc1ci4n5lkXfbVjzj5fxNFPHtq5nqN10c9510kfMTMX9z4yEj/7AqzOkzXsUospZuuVNmKiuznnfj+rR3Nru6OY2No7ZziN+1Pmp5cbAlO0/DpqbIqbh+tRIS1YxuN5KuDUvB0vG0/Ms0ZuDOereB5ORmwf1Uz8o9E8jKGteq0OlX5ds6M6efjUK8eOL4/VSJzWW079MlNH47UfMfTFRn9yW/WHWI6tkzq4P+Gscsv15i4eo5pp0zHMyXydJ4a5Zkxrrx3++DJab2vpXH/mxnNNfuC5hz6t2RV+aSP3VZ3k2LrI69kR3hNmcstcj+JMemmfdbDW7jF2jxFzsksfno9ism8eV7Aa+yfMTy+3nyDCu+TIIfGl8yrORy8a4vuielX8jbtfWrsHjn9novqsLm/3f/q4L7c3+sXJflKjqV/VuMbgU2PHYG1fbtdePK3dI3NrsD+Rv17rR+rylWzpjavfAX4l3p/JZV9ub3S50Rg29XT53NE4q+/cfOFOf8xzR9yN8c+LXK335faPJrs//tHC/njVO+C7aP3jLzcbhU9BR1+v/G7p0WaiqV95yXjBtR77MP3zgnm0Zo/Y25P7cvscvR+pzVew5V30ld5HX0GTicOPv9wmUfbafqnsHtg9sHvgvXtgX25v9seS+8C994Hb9dv12z3wOT2wL7d9uf1//3BkH77POXxb563z7oHX9cC+3Pblti+33QO7B3YPfLse2Jfbbupv19T70/DrPg1vbbe279ID+3Lbl9u+3HYP7B7YPfDtemBfbrupv11Tv8sny81zfxe0e+B1PbAvtze83F79c27vduD4mZ9X/tzfu+lxF19/Z+JdP1O163TPixwd76rJXb3yFXH25fZml5u/oWT/gO8/L4r90vxHiztfMvtye42uH62RP+S/f6nCcX0eutzyN1e8SlgPVP92jOkXBvNSazvm/SneZtD22d+PuHqJri4c4z4brw+BeEfas0eek16N9xlza8SY8dDsLl1Wdcl4r362B+yxHN/1g4hnsWv3rJavrFO+m1J7nlv/tl31IXwT6yNnyrMr3oTVvCbuam+/dW7u7/HB/6w0i330gv2IsNOBcq0b4sphsQmSL3j40kyPcF3FM4aNJl8u2V+/fn3aS9y4f/7559+Xm3weyfFuWzTj5cH/5cUBFx9uq5eKNlfHVV2u+t9h1z1wB+bvxrCf0PcOLq+skxdDnvOJs5dM5sRz9qJ554dk1/odNMXoNXtDbhOW/PPMYn90wcH7GT7N77vOL3/nZlPwPygjqIW6WxgLn81HjOlliE02YHMR68imfY7mq3g2r42Jnfow5sE5wj/aU39jTLbYUBtGOPCVdsynw+DBSnvj+UnT8dFcjMmFqyZwmuopj7NY4GjjONW47TK+unSekz7aHo3dA5OtsTpGrzPPOh7lqK82XR81hV/q0RzkS73Ecsy+wE5M91dYGU/bqU7iTXvyOhvFmGqcvuTScXxPmKea9lmbejaxp+fG1uYKX23kpa+jPM9y1v6njZcutyyQgr9K0IyVxZgaa2rU9BFrdfjS9srzKh7cOLx9GMBEp37hXInVNuCc5YGNBxcubb/iyXpy7EPzER3RDB7E4Ls3+ofcOqbcsq94bl3FEwesqS5t1znht1rjIm79z+byZzyy1c48J23lRe7kAZ7nzrlrzMEwJvOspX6JZUx7Bd+jtYwpN/njy3732motY8pZTZK3e1dH80xe7buyMb45TDmCBbY2jb2ai9V9ARY1mfQQS76pv3uMU81y/6c/X7rcsqgKftREHxHVgmVBjZlrxGB+1BzY2Lh5uJ/lt4pnjG5g4qDTRw4tGJMmnYM21mU6VFd1zHob5yhHbaYRzXwh8KxGjOoid/YTw3VrPOWEfddlZdd5JYeM+8zzI/pkT+SzceXfejR/7XPUF1vWrbkaattYkxbqnzxa64xhTDmAaTzGyTf9m2P6nj2bJ+c8v5LDxEsd+BMp+5FYrOc7w3ninXFif9JVHfgrC8/GhCVfdZ1s5E/+0/5PXju93GwaBe753eJ5oLJBeZ4anyZpO+ZylVtjHjWUPtO4iieHqfHhkodmwj1bu6I5B4G8GMEzZzgnfh+GCRuf1mg6pIm7ek4suP31119/c0u8o0OcfPM54xEj+2NllzHxN+5H6wMW2PZBjhO2tdEOvpmPvFMxhmUAACAASURBVMDM9eafez53PXuuXWvUGmInT/aYr7DarrGNOcVw7xUjPNBYfVPX5jxpqz0YUx2vcE7c1m+lE7jyO4ub+Ff4/CSb08utG7ILdLdYFtUDJT7zLnRz0/ZopBl8qfB8ZNt7q3hiTng0cPNu3LP5Fc2ngzLF9sDKlbEvMm3wh5s1yQvkjLP7aCa+OMTkS12MJyd9GTOHKUdsui7MrXGPxjSG2monV/evjnAHY8phwjDnSVP3Got580cTuedo7czPuVxay9YQO+vFHnN5ZZx81q6xjTnFcO8Vo/zVWP7TvxtobcmB3NQN7szN8Spfcf3OMGu60knexEv7Kab45Dbt/+S1w8ttEm51WO4S0cJ2Exk313m2cR+JL9ajvqt46LRqRBq4X0iPcMVWvh609lczOExf6aetOjL6LK75JNajWokFdl4YYLOWveVLhzX9HPMFkM/uM4KX/FZ26TM9m3fyneymNX2nHNreesKZWK3/Sg+ws5fIs/tObPaI23O5tEatIXbdKyssMR0b2/UphnuvGolpPeXfmhE7OVtLNZQb88nX/Wm0llk37VZ6sE6cjq9fjt0TuffTnw8vN0VG6NVXF0CfXr8qdB8o/WzMxF01hz6rUax8Ia5sc30Vz8PAmPY8w3dq7LY7mq800ccD1PH16zyx48Djx5h++pCr+B8ZwfHlAg7aw8dPsnBYxex1eLaW5p45TnZXc3jWF7+rL77UhP5oP3MCM3ln/6lN5q2+6O05sdedi8c869Jz7MzJXjCmc7F6nDQ0p+aLrxynvcZ+ZC5u8k0Nxeq80KJrgq16tJb6Tz7uJQew5NZY2IHT63LtEbusY+//5Pnh5TYJsyoKtu5RnGcbddUMFL1fbFOjJmf4YANmrtMQUyOmzfS8imfTM7YfsZp321yZHzXx2V7Ht06rfFbrV3i2DVh9+ODLv5xMXpOGrV3yJo5zsLLf7KGO29zA75pNfNtvmk/8JztiZu9NXL0IktuED9fUUL98OaoRcZMP89RHX+2Ys88XcfSVh3au52hM/Zx3nfQRM3Nx79lx0hWszpO1rrk2U09NHLVHd3NO3ubHyLrcEl8eWbvEmJ5XOJPtT1y79XJDQIr7SIFadAsGRn51IxhrWk/MbDzx8lCn7dkzuU3xunk5+MbqcfI/i8u+eXhA9FGv6VClX7+Mjurky6i5M+/48liNxGm9zaVfFOpo3PbLfLDRn9wmXc1RPMbWqW0mnFVuud7cM6aaadMx1MN8nSeGuWZMa68d/vgyWm9r6Vx/5sZzTX7guYc+rdkVfmkj91Wd5Ni6yOvKmPHUo3mL07bm6j5j26Qmacdz1sFat01qC1bnOsUzD8YJV59pr+P/xPnDl9tPFOmr5MxhnQ7infyOXjTE90V1Z8yN9Z+/I2+/tP5Tj90fsx6cx74kt1b/aLUvtzf6xcm+9FafSO9obGP0J32wWduX2z+H5w69JwxrsD+Rv17rSf93WPM7wd0j6x7Zl9sbXW4cOpt6unzuOJSr79x84e5PiuvDdIf+YKj1fnG9Xuu7avaZOPbHq94Bn5nLK2P9+MvNRsk/356eX/nd0qMFpqlfecl4wbUO+zB9zsvWntyX2+fo/ej5+932vIu+0vvod+uxiv/jL7eVMHt9v1h2D+we2D3wvj2wL7c3+2PJfdje97Dt2u3a7R74vB7Yl9u+3P73Z5j2wfu8g7e13lrvHnhtD+zLbV9u+3LbPbB7YPfAt+uBfbntpv52Tb0/Eb/2E/HWd+v7Dj2wL7d9ue3LbffA7oHdA9+uB/bltpv62zX1O3yq3Bz3dz+7B17bA/ty++GXGz9L9epf6fVOhxg99m9hec1Lh5/NuuvnM3edXlOj6az6uzPf7edc9+X2gy83f1j43Zp2OoB3re2X5utemvtye522d/X/CodzsfoFziuf371+ermZVP+2is/4tM9Ll7hHsTgwyS1/cn/FXfvpE/pRTC8D/R2fuRzwmfIyRmK6ZryJ96ON5G8hSb0aQ/3uiNfYz8ytTX/6Vx/4PoObPmD87nytjfXO8ahemcdXfIZ71+5Znp9VJzij/6T7VKej3vE8Tee+dbDXr9i2r3O52z9HWG07nSU4HeVn3K8yXrrcfkdCfiv8559//n0JtNjud8Gwy4tBobWfmrRtVjGnl6hNOMUUdxqxb+7YGUM85tgxikMOH63JKr4xGInz119//f1Ckk/uf/YzHMgbPbIf1CzXnuUGxke1fTa2fr40j3pV23cayeddLjf6gEuB/1SXfrtaC+y6f7Ke7E/nPutoPxP/zDb9fPZdl1q71njGupKfGIlrzK84ftnLDdEpBCPCt/g239UXmoVpnCzKWUwbIWPauI8WfHW5GOPoMrlik3n1s5yPYmhDrth1fkf6o3EeIrX3E2SORxyaN7a8OH79+vUf/aAeWRd84XEWS9+065cTWOar3dRHaqbNhNM5TXNxphjaa9Mxet25dZRb1kfMqU5dHzjx1bq19mDiazzH7qOO2fnIreOBt7KF32pPvKORWPzHqminfke1SCx5qof5OQdn0j4xsEEn+vzMNv18bg6uwyF1kdvV3MABA+3NR+yvOH7Zy42D4UFAyC6yIvfhW4l8pZBnMaemebT55Ueszok9YxzldcXGONOIdtnkKxv5EY9nRm1Xebsuf3W3lviz98wBwQ/e8OflIx/1YB18OWRMbfIg20P64ctza2Nc44mfWKs1bNBA3a6ME9bkN+VEvOQvFnqrx1QT8PkTC3Nkrj7WkjXwwbI3WGt9tEsb1+TAXG6p44Qlj7M6JSYckzd7z3xNHI9wrElyTXtybV1yHz/rB/8j2/TLZzl0/o2XsdL/6PlRPY6wXr136XKjUfLrGcEfScTDZ3EsVjaMNvCyGY5iaJ8HKe3dP4o58fCwJ7fEXT13o2lnDHm4niOxyPvRmGLAOV8yrueIjVrZ0M2J/e4FOGU9zCe5iid+xj16Jr7YPMunY7DevMBNf+vdHJq/XI0lv7ZrDto9MxqzuU1Y8LAX8llbsbrezV/7HNUofeFkDbTt3HuuHb6JNdXJmObec7GO+E8c9Xt0VD/5HPnLNXNse3Cm3sTOWPbapE/jreb40hfydo5u+ojPH71i69cRf3zBPLMxxu8cTy+3JmcBu8Hb7iNzDgcNwAiOMS1UYnugLQwFy32fjzCwuRLTQ2ssxlWjGnc12myJlc+rPDwAz8Y90wG+xsiDMDW0ehzZWZ+0EX+V45Fm9h0YHDDG5GF+0+FLu3zOePA0Bus917b9zYkaZq7aPzImVvYEz5Nm1Ea7PiNitV/zX/Hruvccv8Yi1tSf6Wudmi94adfY8lzVxf27RvWbeBLDPNR/yju5gLOyad16njhXntUObtnT+sKFvczNfKfzo99HeYnz6vHhyw1CikaSryA4icfaVCDjZ5NNhXE/C6kv45WY5u3LCx+agzGxrjxP8fAzxoRp4x3pcBb7TAf8pxcHa+Rq7tg1lvwmm6wJuT2TQ/tRS9bUjLjNKfXQrn3SBozkhi15r76mXLVNnIxx9qyOq15tf+2nl6Z75JF+apH8XZO/Y9YOTjkHUz+xiDVxSV95GaNHYzS2OXSdXL97lOfVWsCLXFpveYEzaTPludJRrKMR3+RBXOaZx4rLmbYf4XXE+e69py63Rwv+CGlfTt3szldNYwyL6kFzXdwsbu8Zo0djdgOKOTWr2Ktx1SDGMKb+xoJb56bNlVGcSQf92WsNnLdf5gGv1sJe0Z/x2Zc+sdIXrfjXnH/88cff68Q/yk9tsctn82ZkL2P0PG2PnsVPrCP73FOz1jptfDZf/g6SLy8F98XqfpIf+WHrvGMyT8yep69Y2RPyYExfeXe8tJ+w3X+2LvpfHdXvjGfiZZ65zjN7fUZWWqx0bMyeow3nrGvOnPWzOp1p+yyv5vnq+VOXm+IpUpKkeJOwaXP07CFrbBsgD9qE0wXURv+pSa/GnOzUohvJuKtx1SDGSDy5Z2OucK+sHx0+D3PGF3M6mNqjA/ut7ypPMR8ZwcrLAl243Pg7A9btmVXMXJc3a3JQ54xhPcTW9sr4rK/cWsspZmoy9aJYmSc4qYXzzNtYcMgz13PsOk94NJY2Z1jGdZz4T3XSnhGOHT/3H3k2/pVaiDtplHt9uakN53v1tfLpdeJQ2+ld0f0x1Un/CTdzyDq6/tXGhy83CzEV20ZA2GeT70OXgrFn0/JMcXLf+FNsD8TE+2pMc8+44h41Q3L0eRXTGOxjK/7UrGI9Oq6aGpyzvYmHhzn/BaOcjvC0uTqiifXXB3y0Z51n1u2DrHXrih37WTfnrGFvDNY7rnuOxLZmrk183TsaJ/6TPTGpR8ZtrmKlzaRFY2Xf5XkCP+fwEm+lvxz6O0v9wJzyc439K3XC3liti1iPjuKdcRQXnacz4n7n4vo0gpV5p41xpljqmnWyntnHrqWdvtkvGfdRPdL3s59PL7cUESEnMZM0xcNmJU7a9rNirxqphTeWvI7irrBX63LLmD57iLXpF4PrRyP6TI1rDPUTO3P0ORv1KFbv2aDGyH00zWbPPf26PnJc+U11IofGyVjTM3w7ZzmBl3XJdfXKffCtvfvgo39fbtiyp51j59s2U32nvHpt4m5MNbNPOoa+6uRcf8fWYsoRG+Jlnj3HTy6J6Rrx5II+iYXvFX6P1AlMOBqT+aNfK06tXeboXucnH/d7tJ4TR/Tq+mpn7LP9jDfZtrbYZx2N58jeR7QV5zPG08vtM0jsGI8fwI9qxsH5jCZdvWg4JBwkeHw0l+2/7h9f1FvntUa7f65p40V4dCF/JS335fbEJ7uvVMBnufjSmz5pPovZfh6GKYafPPdL99qLpbW9OrfOW+fX6ny1Hu9sRw99xgfiuzTal9sPvdxoIC+YV34Sm75z89J7p4Ny14H7bJx9ue1L7Y6e809ajv7I8o44d2Lsy+3Gy80XSf459/Q8fSdzZ1EfwaJZpz+LfwTjzJYLrnX4Shqc8X/nfXtyf+e2L7ln+9gPo+/WQ/tyu/Fye7Z5tt9+8ewe2D2we+DeHtiX277c9j/o2D2we2D3wLfrgX257ab+dk29PwHf+wl467n1fMce2Jfbvtz25bZ7YPfA7oFv1wP7cttN/e2a+h0/ZW7O+7uj3QP39sC+3Pblti+33QO7B3YPfLse2JfbD2/qz/hRgHf6RIoe++fv7v0Ebf35kZC7fgRk1+k1NbJWOe4fBfjhl0Q2w7s8+0Pc7/bzK6/Ud780X/fS3Jfb67R95ZkAm3PBz6oyvjrWXfiXv3Pzh0H9YdxX/+AvCfLSJd5RrP4BYeaKY0Hk3OP0Cf0oppdB4zxzOeAz5WWMFab5fvQTsPVMvdTNUf0mnbT5zNHadO5qdsfBA+N352ttus+YH9XrM2vxTCy4d+2ewcHns+rkeVvp7nc11uqsd+xV7Ff9ehbzqmbiyG0VD7wrtpy/s/yucvsMu0uXmy+VI3HuJmvT/Pnnn39fAh3b/b4gsJsuBu1XTQp/bVYxbczkojZTzCNNsG/u2BtjwiOujfrRl8QqfnJGK/6/NGJNfNL2M57hwOFCt6yBmuXas3zA+N0H2MvtqFefze93+pHPR/tW/q+uE/icNf6vQPptqsVUJ/0Y5ero+8Uz3Db6HsUU62g0TmrtGelz7PqUX8eYcNvmK81PLzeT70K8Ogni0lSMCN/i2whXeVmYxsk8zmJOWtjg2UiJuXpeXS7G6CZM/uTwaLzkIeeOMdmgL3Yd70h/+OXFLXcPdY5HHJIPz9hy8fz69es/+kHNuhfgcRZL37SbLjfz1W7qI3XVZsLpnKa5OFMM7bXpGL3u3DrKLesj5lSnrg+c+GrdWnsw8TWeY/dRx+x85NbxwFvZwm+1J97RSCz+7zm0U7+pFqyt8ul14qERvPo/12Xvaswj3u6h+1Rf+Oa62k+5idWj52Cqd9v+7vnp5TYV8DNIUyAbBCGzKMRX5D58K25XCnkW0wOWhT1q/hUX1lcNaIzOK+0/WhP4nx3+1BxO6M9oTqu8XZe/ultLc+fllDqKezSCCW/88j9GVTPx5JAxtcmDjH3zYK21Ma75i59YqzVs0OAor96bsNqG+ZQT8ZK/WOSpHlNNwONPLMyRufpYS9bAByvPY+ujXdq4JgfmcksdJyx5MOLH11SnxIRj8tbv0XHiCIYaJnexidu5i8Oedct89GXUdsJOu9Uzfqmzdq1Zz7U7Gj/K7Qj77r3Dyy0LiGA0jF93NM4qGeMaY2oGbeCTh/kMc9Uw4h3FnHioy6pRV3yI0wcAW2PII9eMsWreVaxev+KPDV/42tDJiXX2O4c+MOYj98QTv/mt5sS31jzLp2Ow3rzATH/r3Rya/yr3tmsOqxyurBuzuU2+8OAMMOaztmL1y675a5+jGqUvnKyBtp17z7XDN7GmOhnT3Hsu1hH/iaN+j47qJ5/073zcyz5zLW1X+mh7FFObo3HSFfvuD+34TtL3OmPWaIqTuUz7X2Xt8HJTZA+PpBUJcVy7c6T4vJwYwV01OHtysTgrTkcY4FyJaVMai3F6iV7RAp6J08+ZRzdTz6/E0+ZMB+ysO9rqN8VUjyM765M24meOxjkasffFCgaHkDF5mN90QNMunzMmPI3Bes+1bX9zoo6Zq/aPjIl11BdiUhvteHadUazWuvmnTz533XuObWMRazoX6Wudmi94adfYclvVxf27RvWbeMIB3VNb+WYPuWZf9Ly5HsVs22kufnIWM/uTfeaT3XR+jLWqr/tfZbx0uWXyEmftSADtnhkn8VjLhmlcDwvFmni5P+UC1pWYNo1Nik83d/Nazad42BqDfebTIf6I9mc6rGJ6kM0du8byAE02WRNyO6ol2NNX+6EDa2pG3OaUONq1T9qAkdywpcarrylXbRMnY5w9q+OqV9tf++lCcY880k8tkr9r8nfM2k29p59YxJq4pK+8jNGjMRvbHLpOrt89ynNVC3gkd3jzd8LmP/XjKie5n8XU7mg0htzg49/1sYcvOckzsc60XdU3Mb7C8+HlNhVG0tmort0xGtOi9NiHtGOyj48HzX1xpyZ1r2M5N6YNI7Z+U4MYdzWuGsQY7NvkxhfrI9rLedIh8c29x/bLPNCltTCHxHn2pU+s9EUr/jXnH3/88fc68Y/yU1vs8tm8GdnLGD1P26Nn8RPryD731Ky1ThufzZe/g+TLS8F9sbqH5Ed+2DrvmMwTs+fpK1b2hDwY01feHS/tJ2z3n62L/ldH9TvjmXiZ56SFWqtX+vL8TMzGmObNpef6nGm78tP/q4yHlxsks1CSPmpM7HmRIYD2j4yrwhszD9qES1zid+PoPzXp1ZiTHXGeyXfVIMZgX+y8GPr5TI9Jo6mm2nmwpvrht7q84Mp+67vK03iPjGDlZUFNudz8RGrNVzFzfcrTHskY1kPsR/g+6yu31nKKnZrYL6xpK1ausZdaOM+89YdD9ljPses84dFY2pxhGddx4j/VSXtGOHb83H/k2fhXagGu9mggzz6zPe/eEuMopnr2eVzlJpfsg6lO+HdvNObUA23zFeanl5sipig8T81jUSheNvEjiR4Jm3F5XjXFFNviTg1zNaZaZFxxrzaZWqxiGoN9bXv8aHOtmpo4Z3vUNvPHRz75LxjlfISnzdURTbrvwEd71uVlH2atJ13Zz7o5Zw17ebHecd1zJHbXbOKr/dE48Z/siUk9Mm5zFSttJi0ay77uswx+ny/xVvrLob+z1A/MKT/X2L9SJ+yN1bqI9ego3hlHcFvDVSzzVq+2uxKTepIjXysccY3XOVjjrKe22S/iMF7hlva/8/n0coOcCStmNlqTR8BnG0uxuwjGkIfCG0teR3FX2Kv1Kabxu5muNrWYjOQw6WgMc0wfn8k7G9L1q6MNOsU4wtav62P+K05TnahV45zxh29fMnICL+uS6/ZH7hPL2rsPPvr35YYte9o5dr5tM9X3LEf2J+7GVDP7pGPoq07O9XdsLaYcsSFe5tlz/OSSmK4RTy7ok1hHuSbWI3UCE47GZP7o10qz1i5zZK9rsYqrX+Z4NaaYYkwxG+tIi9aWPJKX8RzZO8LT7iuMly63r0B0c3j8kB5pxovmM5p09aLhkHCQ4HHEc+99rO6+6LbOH9Nx9+E/HwY50++gx77cnvhk9w6FPePoS68/SZ/5PbLvp8Iphp8890v3tS9d67x1fq3Oj5yLd7Wlhz7jA/Fd+uzL7YdebjSQF8wrP4lN37l56b3TQbnrwH02zr7c9qV2R8/5Jy1Hf2R5R5w7MfblduPl5ovEP5tfjdN3MncW9REsmnX6c/tHMM5sueBai6+kwRn/d963J/d3bvuSe7aP/TD6bj20L7cbL7dnm2f77RfP7oHdA7sH7u2Bfbnty+0t/nJ4H/x7D/7Wc+v53XtgX277ctuX2+6B3QO7B75dD+zLbTf1t2vq7/6JdOe3v+vaPXDeA/ty25fbvtx2D+we2D3w7XpgX267qb9dU+9PteefardGW6Pv3gP7ctuX277cdg/sHtg98O16YF9uP7ypP+Pn3N7pEyJ67B8uf813Nfy8410/37jr9JoaTWd1/5zbD78kpqb46mv+hpJ3++HMV+q6X5qve2nuy+112r7yTIDNueAXMTC+OtZd+IffufnbDfq3Szi/61PYKhleusQ6+g0a/dsvmItnQeTb4/QJ/Siml0HjPHM54DPlZQwxpxpMvM356ihu6tW+6ndHvMZ+Zm5tuu/U7I6DB8bvztfadJ8xP6rXM5p+pg/cu3bPxv/MOtl303n1u5qs1ZSjZ0m7VR1Z14bxoz0tdzF9r6TuHXOywZ713302kvfZ8+HltnL28K1EWPk9sm7T/Pnnn39fAl1k97vhsJt4ab9qKrhps4o5vUSJReNMMY/yxb65Y2+MIzxy+GiTreInZ+Lwn4FyWI/4pM8rn+FA3uiW/aBmufYsDzA+qu2zsfXzfB31qrbvNJLP9OJ/JofPqpO9xRnv8zrVybXM074Fi1x9z6TNtGbsZ87exKN1Nmbmha6r95n2ybsxv9L8qcuti/WKhCgsojNyKPqgWwTGK/EtTOOk71lMmy1jXmmijOEzGmZTuW6Mo4bWJnnof2WU81EMbYiBXTc06xyCiQMaZ25qj31/HXHoXLDl4vn169d/9MNKD3hkvCmWvmk3XW7mq93UR2qmzYTTOU1zcaYY2mvTMXrduXWUW9ZHzKlOrRmc+Grdpj7A13iO3Ucds/ORW8cDb2ULv9WeeFdHsOBMz7Vm5DzFIW9t5d36MCcH19MnuRFfrFw/e5Y3+q5sr/Bv3+bd+19p/vDl5mFBvFcmQrE9CAjaBVZk7K7w8BAd8T6LOTXqs3qsmtkYR3lpgwZXcm8b/KZDmXapOfHQn1GbVd6uy1/drSX+7OXBFvNsxA/ecMv/9bv1kEPG1CbrD07zmLQxrvmLn1irNWyOXjBTzhPWZDflRLysrVjkqR5TTcDnTyzMkbn6WEvWwAcrz2Pro13auCYH5nJLHScseTDix9dUp8SEY/LW75ExY4DV+Uy8wCcf80yMjG3uckyftFv5p00/2xf49l7Op5jy6nOhn/tZM/e+2vjw5TY1391Jefgs/FQsbShCHuYVF+1XRXH/KObEA7xVI6y4sE6cPiysG0MejSFPD0/vX5lPTd1+2KiVDd2c2O8c+jCaTx408cTv2Ks58a01z/LpGKw3LzDTXx2bQ/OXq7Hk1nbNQbtnRmM2twkLHvZfPmsrVvdL89c+RzVKXzhZA207955rh29iTXUyprn3XKwj/hNH/a6O6mbdJ65gEQv9tevYKy3EN88V/lTTsxzU5t///vfftYIfX3kmJl3lih+25tTx4Jx17P2vMn/ocuuCvCoJREZcRmJMhTC2xbeAq4IcYYB1JabFN1Y3jJyujPBMnH7OPOSuTTbplVhpI5aHKvd8ts5o69rU0OpxZGd90kb8zNE4RyP2vljB4IAxJg/zmw5f2uVzxoSnMVjvubbtb07UKHPV/pExsay546QZtXG/6ypW+zX/Fb+ue8/xayxiTT2avtap+YKXdo0tz1Vd3P/o2Dn0PPHhov6dt3n2OjniY/7m6Rx8a4fdIz0FV3zyDDQP58bL/IzLWubpc9q69hXHhy43ksqD/6qEJvHOYlusLqoc3beYrjteiWkD2mj4EI9RnKvjFA9fYxxhepiObFY8znTAD/yuszHNHbvG8lBMNnnQ4N34K7653n7UkjU1I25zSn/t2idtwEhu2FLj1deUq7aJkzHOntVx1avtr32/QLFzjzzSTy2Sv2vyd8zawSnnYOonFrEmLukrL2P0aIzGNoeuk+t3jFPMo5zgDh97j3nqnevmOX13ZFxt0NDvvti7mhuxp94TP7lSk6wLMaxN5pCxV1qkzVd4vny5mTBCvJL41AgWu5tm4oHw2HnQtBF34u9exslni5zNAa5+00E27mpcNYgxjLny74Zc2fW6nCcdtGUv88/n9ss80Ly1sG8SYzp4xj4aiZW+aMW/5vzjjz/+Xu9D21hqi10+px17GaPnaXv0LH5iHdnnnpq11mnjs/Xk7yD58lJwX6zuJ/mRH7bOOybzxOx5+oqVPSEPxvSVd8dL+wnb/Wfrov9qXPGacmKNvjZvMcnprO7q3b5iOE5x3VuNK206Jjzh3zVou47zDKfG+Iz55cuNhM4KBmEFw/6ZBFbC2nR50CZ84k4Np38XEoyrMSc7Gol4j+aLfV8EyeUMjzzOtJj0Ye3Id/Uy1K85a48O4La+qzxX3I7WwcoepKZcbn669UWxipnr8mbNmPZIxphqrv3Z+Kyv3FrLKV5qMvWiWJknOKmF88zbWN0rPceu84RHY2mTPTthGddx4j/VSXtGcDt+7h89y5MzvfryDKzioO30Dsq42KQWueezeXbt2JenXPTJPc+De12XnmvXveG645W6afs7x0uXmw1GUkdktaOwZ4Vb4RwJy55Ny3MXz/hTMp0x7QAAFoxJREFUbBtlyuFqTBsq44o7NdkqR9ZXMY3B/sqfvbPDs/JlfdXUV/amuDZ7/gtG4x/F0ubqSN7WXx/w0Z5162IfZK0nXdnPujlnDXtjsN5x3XMkdtds4qv90Tjxn+yJST0ybnMVK20mLRrLvu6zDH6fL/FW+suhv7PUD8wpP9fYv1In7I3Vuoj17Ih+yQEcNUv+xm9b46rral+7M23gQ458qbu+jK2ZvJKrXLKe5jRhgjvhZNyv9HzpclPIVcKZEOI921iKnQVIbAvuQTWWRT6Ku8JerRs3Y/rcOtgQ8tL3aMR2anBjiOU8c8xmPIqx2rNBjZF2aLrC16/rY/4rv6lO5NM4yWN6hm9fMnICL+uS62qX++Bbe/fBR2/qwpgc2NPOsfNtm6m+ibl6nrgbU83si46hrzo519+xtYBL88eGeJlnz/GTS2K6Rjy5gJ9Y+F7h90idwISjMZnf8QX31hpcclZTx84RPu4xgtWcWocz/uo7cRL7StzWFn5ZR7Ec2Tvjpu3vHi9dbr+b5I5/zwFNHTlgn9GkqxeNL4XpoCfP/fyx2vvS3Dp/TMfdh/98GORMv4Me+3K76ZPdOxQ7OfrS60+ZafPRZz8VTjH85Llfuq996VrnrfNrdf7oWXkHf3roMz4Q36XFvtx+6OVGA3nBvPKT2PSdm5feOx2Uuw7cZ+Psy21fanf0nH/ScvRHlnfEuRNjX243Xm6+SPLP16fn6TuZO4v6CBbNevTn9o9grWy54FqHr6TBivd3WLcn93du+5J7tp/9MPpuPbQvtxsvt2ebZ/vtF8/ugd0Duwfu7YF9ue3L7S3+cngf/HsP/tZz6/nde2Bfbvty25fb7oHdA7sHvl0P7MttN/W3a+rv/ol057e/69o9cN4D+3Lbl9u+3HYP7B7YPfDtemBfbrupv11T70+1559qt0Zbo+/eA/ty25fbvtx2D+we2D3w7XpgX24/vKk/4+fc3ukTInrsHy5/zXc1/LzjXT/fuOv0mhp95KzySyH4mVnGj+Dc5bsvtx98ufkbSt7thzPvav4JZ780X/fS3Jfb67Sdevl3rFHjV/9SiKt5XbrcfAnmb5n4jBciMYh5JFb/9gvmJs+LKjn38/QJ/SjmpAOYz2iBz5SXMRrT3xLwbDw1cfQ3V6Re7jmq36STNp85Wpv+9K9m8P0on69wuVmb7lfmR/X6aO6v9od71+7ZmJ9VJzhf1V3bKUfPkjXtOub51oaxe7pxsJniXdH1qM86rnietYkbNubxLCfj3DGeXm6Kmcm61i/gOwiJoUh//vnn35dAxsfG/b4gsJt4ad9NZbzEXMW0sMnFF+4UM7H7Gfvmjo0xEo9nLhj/U87ca9yr81X89Ecr/jNQGvWOmIn9zLM6oFvWQM1y7Rl8fMD43Ze5L52jXn02v9/pRz53vfReXSfweYFz5ui3s1poP1029i19iv6+i860wG91iVhHe+UMS/sc9b16tuUNpyNenseruMnpzufTy21qSJM8K/hHiCIQTcVInI5lMzFeiXOF81lMi5YxbZBHm4vCX7nciCW28T/aNHI+wtGG+NjJQa1ZXzU4tcrc1N5DkeMRB2M5YsvF8+vXr//oB3XJuuADj7NY+qbddLmZr3bdj8RTM20mHHM5GsWZYuinTcfodefWUW5ZHzGnOnV94MRX69bag4mv8Ry7jzpm5yO3jgfeyhZ+qz3xjkZi8R+rop36HdXCHNQmc5R362M/9XryMnbXIG14Zn+qZ9v1/Cq+fnBFVz9kH3FHi2c4GeuO8dLl1iQfFeUZohTMJkHE5sAaDX5WeGNnA7rW41nMqVHV4qj5Ow7zVUMaY8rraG+KsVqzScE7slFz7HhO+1Xerstf3a2luVO7o8Mx8QKTw4Vf/q/f6iKeHDKmNlkn7JsHa/1iNK75i59YqzVs0GDKZ7U2YU22U07ES/5ikad6TDUBnz+xMEfm6mMtWQMfLHuDtdZHu7RxTQ7M5ZY6TljyYMSPr6lOiQnH5K3fo+PEsTGIY67kkjme8TziaOwjG7hk/OZ2NL+KD0ba2ndZj47DXp+ttnn1/PRyMykPjPMs4N0kPXwWdRJTGwSU2xEP7fMgpb37RzEnHh72o0JnHJ9XDWkMeWjPeLSXdmfPfQAne2zUypo3J/Y91GL0YZZz6iOe+PqejcS31jzLp2Ow3rzATn/r3Ryav1yNJce2aw7aPTMas7lNWPDwJZLP2orV57X5a5+jGqUvnKyBtp17z7XDN7GmOhnT3Hsu1hH/iaN+j47qJ5/271w7x97X/wwXO7CmPhaDUfzuz7RZPcuB/skvtG2fzMuYk51+Yj/DS4yPjqeXmwFITgF4dv0VI+JRVEbwVw3OHgLLi3El5hEGOFdiWtSMd9Z8K33gmTj9POVh/GlvFafXz3TA3sbM5s3mFlM+R3bWJ23EfzQP7H2xgsGLkjF5mF++RCe+6eM+IzyNMc21bX9zoo6Zq/aPjIl1pS+OzqZYrXXzX/Hruvccv8Yi1nQu0tc6sdax066xte06uX73qH4TT2Il12lunq0HftS2cV1nL/sw81ITe6Mx0vbRZ2oHbvaL8ezrnk8xzPtOblOco7XTy83iWhwTWwl/FOzq3nQ4WDuKqZgUZnqxub8S+0pMc7fI+HQjfCRHfI0BdmMd7bXtan6mA37Ti4M1cjV37BrLXplssiZntVxxbz9qyZq6ELc5JZZ27ZM2YGSfYUveq68pV20TJ2OcPavjqlfbX3vPaO67Rx65rhbJ3zX5O2bt4JRzMPUTi1gTl/SVlzF6NEZjm0PXyfW7R3lOtZg4ZI5ysSczR/+hStdFH0Zzn2KnHfvP9lri8CxX9XeeHORlvRsjcdJvsnvl2uHlZmLdqBZcAe4kaMxshHw+agZ4sI99Cy/uJLZ7GSefjdlF1a/1uaIHmJOfMYyZWEd7aXf0LOdJB/3Yy/zzuf0yDzTvnOyVxHj2IBIrfdGDf835xx9//L1O/KP81A+7fDZvRvYyRs/T9uhZ/MQ6ss89NWut08Zn8+XvIPnqMylW95P8yA8s5x2TeWL2PH3Fyp6QJ2P6yrvjpf2E7f6zddH/6qh+zdP11jVzPIqh3mq2sl1pmfYrLmnzyDM5eI6n+Fe4X63vI7wetT283BQtm5sAEleADIowvMi66Glz9LwSzpjNpbGIS/xuGv27SfG/GnOyI84z+U5Nk1wm/Yw/7bUOR/OjA2jNpxjZ9OJrjw7st76rPPV/ZAQrLwtqyuXW/3prFTPX5c2aHOyRjKHm3U/6HI3P+sqttZxipSZTL4qVeYKTWjjPvI0FhzxzPceu84RHY2lzhmVcx4n/VCftGeHY8XP/kWfjdy3UOj+09XPm2jHR/2hf+66T6znKsWuMDbwfeT+JhZ86d149n86GOBOn5P7K58PLLcXJBCxsF9yESP5K4abEjorJnk3Lc3ICy/hTbAvVnPG7GtMDmnHFnS76KT/XVjGNwb62jkd72lwZ4a+ObX+2R20zf/zRFM3zXzCKe4SnzdURTZo3+GjPurzsg6z1pB37WTfnrGEvL9Y7rnuOxO6aTXy1Pxon/pM9MalHxm2uYqXNpEVj2dd9lsHv8yXeSn859HeW+oE55eca+1fqhL2xWhexHh3FO+Mo7qSPe4zqmvnkfj53TXLP5yM8uXcN9e3xCCttrZv1zj2f5X5ko+2rxtPLjcAUDIHyKw9LktN2tZ+2/ay4q0ZSVLGNdYXXCnu1LreM6XMXzELKS9+jEdupwY0hlvPM0eezF+4qvk1vjLRD0355ua9f18f8V35TncihcYyzGuHbOcsJvKxLrqtX7hPD2rsPPnr35YYte9o5dr5tM9V3lVuuT9yNqWb2RcfQV52c6+/YWkw5YkO8zLPn+MklMV0jnlzQJ7HwvcLvkTqBCUdjMn/0a8XpSDtjTPqwpi8jOmjvOMXs2mLbPbbCE9fYU8yskfyw13c16pf1bttJh7Z59fzS5fZqEhv/8QP4Uc1o9o+8AK7Gp8mnOByMs4N5Nca2W/ePL83p5bZ1W+u2tXlemyuX32fouy+3Jz7ZfUZhXh3Dl15/kr4zrp+4pxgegP3Sff4lcqVW1nnr/Fqdr9TiJ9gcnfnPzn9fbj/0cqPRvGCu/FHEs405fefmAZi+o3s2zvabX977cpt12f3yGl0479Mfp/4OvfflduPl5ovEP79ejdN3Mr+j+MTkjwdf3Yw0fGvxlTT4Xdp/Rlx7cn/n9pqX+WfU8F1i8GGZdwnjV+C8L7cbL7evUNDNYb/Edg/sHtg98F//sy+3fbl9iU9Z+zDuF/Lugd0Dd/bAvtz25bYvt90Duwd2D3y7HtiX227qb9fUd37621j7u4ndA+/ZA/ty25fbvtx2D+we2D3w7XpgX267qb9dU+9P2u/5SXvXbdftzh7Yl9u+3Pbltntg98DugW/XA/ty+2BT8/ND+2e2/vnEyc/N7R/O/kePuz6J+oPvd/3APTi7b++v0131PsKhdnf1wVGcd9/bl9sHLjd/PyLjuzfCXfz35faaF+a+3F6j6119/5k4/mah/YP5xz1x6XJTTH/LxCs/8RmrL4zV4fY3MMiNsYsupjZ3fGchZsfKJvfyuyNe4j77DFc06PqZS2v+TJyvcLlNPWHt3/UT76r/n6kRPp/1nRtx0H6le9dqdVbEOaqjGmkzYXkmtWHs85CaGnfFP22Pnj1jxl39ViDjndmZxx1n9oj3O++dXm6TiBRgVZyPimETdNFs3GwyueUa8fnPK8HhWZu8hMDCh4P1LF/8jw4FuNjwn2lil/GfjflRPzhw4Kld6rvS/Jl44E4vlWewnvXxhdl98SzeV/Cb+v8jvK7070fwPXecRfptqoV9l3s8d/+wljaT31RzOWSvd0769VnW94h/Y63mYvkOsJb5DnUtebiWdhkDTVZ7afdTnw8vNwtvURTJ5up19z8yit0NaaFtcrk5n2Lqkw0z2T26tuKYOPIjD3RqDqvG1C/zMg8/zeX4SA2w5cXx69ev8WWRmsvDWP3CMVe10I5xsiV22ky8r8Y09moUJzVsW3n3y6HXxbKO5tB+4OurzaQDnPhq29RertiJ5dg5dW9MMcFr/cHrnsy4KxxtjkZy4z8mRTv1a974s9YczGeyz5jsZw2OsDpG4vCMNol1lX/jTPNVPuriObAfug+Yr2qhjxhT/J+8dni5KV4LvirYHUJejQknDmhzSw7yzMbN/Wef+zBMOPAyLjnxzKjtij/r2czmkAeU+Ge5GydH/MAmRv6v2a253PLQTDG1YzQOz8mf9X4RGS/xPez5UmONORqIf2WcsCY/+ctDra0bPmLlZaBd1mTiCvdJC7AyBvHTbsJ3rfUBJ9caixzYz3iuJX/1yXzVxb1nRvGSIziudwxr0nw7duY0aaM9+GdYRzbybP7in432ep4RfIiZPaVd63HEzbynOp7x+gn7h5ebhW3BXymqRe5mMKZNls19VCgPC42k75H92V7zWNkTy3iTjq5pIw7zbNZJj5WvGKuROvoS5dm6ZoxVfq7LzXnzR29jwCOxkxex86Wzskufq8+P6NOaJHfiiWXecug8Xc/RnNSZPfTqGNrZ8xP2pHdrCH7bNbb8us9cX3HM/Uee1a/7ZOJlPvxRYGuUMc0xa7LKJ+ubGD7LI2vkHuOKf9ocPU+1lCt/gpJnAA75nnJuX0xxsEmMyeanrh1ebohCIbrRFD2b6y4BbbYuqA3tIWG8WlR9aRy+rvpNOdnsaDDts6ZN5mBDw0W/bkz9EhsMOCfWZCfm0QiutQSD+jGm5j4nBzGTr3bJCzvmxmCePuJMdubUuabP1efEsuaOnVf3Ru+L1eur/JPj5Dv1QWNNNvJkjxg9z7jpv9I/bdL37mc1kLf4mXPn0j2kjyM5Uc+sCT69ZozsRzBctyeam3EYV/zT5ug5cxFL3lNtklvznuIk/rT/k9dOLzfEofg2AiOfOHgxHjXFs6JaXIqWGH0AiP3MJeUhII+OkfFWz92gk93UcMbNmJ0re52TeecHCQ7FlcZvbu2Hhqwlj3w+8l/Zde7dO9lHnYO5atP7zWc1t0ZX+9NcUmOxxUIn1xj1yXpiI/cc0xdOHaexJhu1MSd5ZZx8Ngaxu6fgP8XI/O56lqe8xTVn/8FGatQ9pA+jGjcee/i1Bv3dUWL5DNaq11b89T0bzcXvRrtfsjbmphbwIp8pV+OKj56u7fH//YjApcutxbLgFqH3PzK36bMJwOvDbSO03ZXY8vcFcMVHG32Pcrcp86D5nI3aObGX+8Q0nv6Mq4Mox9UI5/RFa/415x9//PH3Olqu9AcTfw/jyq4PW/qseE3r4iffyW5aU7PW8siWXiC39hGr6y0/+499auOcWJMv+N13jTXZdK/0fMqNtZX+U4wVxkfW1WCla2t2xBltsW/9jvhdyVOOXWNw3Wv+RzFzz9pOfZzczK05TH2V+PhN2GnzU5+futwQ1JdcC0fBaMAuUtut5jZD+9tkrmv3TNOJ9cghke/ZS0VseerHCNfWTS3Jhz3m6QNO++T+I89g5UEgFy63/FS5yq/Xpzy1yRgfOXzWuDU5y1luV3oja4I+/bIVq+uZdTHv7qfJl3ht13kmtrmiAdwypwlLe8dJf+M1D33AzRq6/syoBslbnIm/Wra9+a84i5mjsc/6R7uuMVjuNZ+MI+fuHWzca39xjck4+Zu3dhmXZ9bvej809rvPH77cKNKq8S0YRXqkCVtEYnTBpjUbohuHlzUHGD7s0WAZQ7+zpk+ffD5qKDBX+tioGVfN4DlpdoSXnK48w7u5gY/WrMuLsQ/a5Ns1cQ4e+sPJw931bL7EJEauTzFzf/Wcmq5sWAc/85y4ipXcvBxyjdxTW23Ab7uus7bq71w/5ujHF3HMSbtcc89R/to451/LNg983G/e4j06imf89Je/ebKHXfeK/TjxTbx81iexc9/nqebuMR7x18480GzKUy7W15iZjxi5pl32lTEZ3U+f3P/pz6eXG81B0fyaipcisn/HwRDHuKsC2hTadexpvw9P8r/yLKbNmj7wXnFdHRRzXR1E9zNHnlnP2GfP4PdBkRN4mY8H0piTZh4ubcBHG2wZk8+UQ/PvXptiJubqOXOSm6Mxza9rZW2NvcJKreDRWqgBY9aV+KuYiSk/eMsFX/mb+xV+5gSW9YdT8xCTGNq59si44mQNMs/klrkar3UVw1E9znDE6x4DJ+uD3SP8sU+OmZsxGbOexJy07xyws/aJ5bP2q5ja/dTx9HL7qcKc5c2hOmq8M/+r+6sXjYelD+ZV3G13/Hvp1McX3db5ml7qtsfX68W7Ybokt/Yf+AclW7x//rWcnxxfoYmfCKcG9lPbfum+9iWyL7fX6vuKc/MTMP1wu79rW/fn/s7thv8V4JUXzPSdm5feR/7o6Ce8AO7IcV9u65fHHfpujMf13R9sr2m2L7cPXG4cTC626TurOw8tF5x/x+D46ph38n9nrH25XXuRvHON340774NX/onRu+mx4rsvtw9ebith9/p+Ke4e2D2we+D39cC+3Pbl9h//qnEfxt93GLf2W/vdA/f1wP/57//+7//ZX1uD3QO7B3YP7B74Tj2wv3Pb37nt79x2D+we2D3w7XpgX267qb9dU+8/2rnvj3a2llvLd+2Bfbnty21fbrsHdg/sHvh2PbAvt93U366p3/WT5ua9v0vaPXBfD+zLbV9u+3LbPbB7YPfAt+uB/wuD3m++MDtAAgAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "AVERAGE DETAILED RESULTS FOR EACH ALGORITHM :"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png) ![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ANSWERS TO QUESTIONS: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "D) BFS implementation using the H2 heuristics outperforms the BFS using H1. It is faster , explores less nodes and the path length is lower. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E) An admissible heuristic is one that never overestimates the actual cost of reaching the goal.It always provides an estimate that is either equal to or less than the true minimum cost to solve the puzzle from any given state.\n",
    "\n",
    "H3 heuristic:\n",
    "Row mismatch: Counts the number of tiles that are not in their correct row.\n",
    "\n",
    "Column mismatch: Counts the number of tiles that are not in their correct column.\n",
    "\n",
    "We can take a counter example to show that H3 is not optimal: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "EXAMPLE STATE :"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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OQTK2ilWX9TO7X5kjG2uM0OtPlhdKiCQ7i7SA2T5ml5XF0vr6ms71fwPuexe9ykUIBlbgZ2vGbv1n+5U5sjH1VszSQtkjkii69+/f//9eDO5J4vc9cYVYVm0M0VVjufcL/Nj4vH7lIkQ81uf7+Kr8LqF8+c1TLx9LC2V0sx+J+vHjx9veDWXck9yygWSq2FYoRAY3CKCNLepLKBl0X5+D+rjHF/uQ8xk/e7X32pu5v9m4e0deViijeyyYKR59KOMlDcCErYqNIbpiHNYnLLn3ZvktbgmlRY7rY1XV8GzbyuLGRemf1eLFtreFRzLGegfNOC66jwUBZZqXOMCgYlFW54bBHw/RbFzoR8JZkRMbs43D7q/U9/K9kn8jfWH4WVIocW/SBtv6IJ9tmIU2O3Zbcflt/WPjrXSehz1EMlo1SCjPs+dNNM5bXcMCUz9LCmVUQEeX3Pe0WgBbH8vyaq35hu3qDcs9b+b45cuX37N5G2vrSyjPs96wbFsI57O0FjO2vS08kjHWO+jZ4zDLs/61/lm7zY7dnpmlnvUnOt/6Fx2zyn5vCdgwhyDaWFtfQnme3YZl2zbMz1uub6HFjG1vC49kjPUOeva4mUKJe2fVWmVujmCFWaONBX3MLts7rBLKI2j2H4tZ/D3uEspt/JYUyu2Q+E/vkwe/6x4lj+fWmdGS294+kVBuIch/5uFacULAR7h9pq3z7SP/fSqh/IuF90ABgNrC/QfbY3sM0Y/1+L+je++v3herV9CIHfsrt+r8eLhWnBCM4pjhR0L5lw3vXpldBo4ijbHLEM2MM+oc79aJh7VX0BLK86x4kwIJ5TauEsrbLXwNpWryrCyU0atd3sxdQrldvOyn3oUK94ufpTH18/RCGb1qhKVhe6hQLYEYoqvE4C258f1ur0koPVTO7/OEEli3hrxHXeDVOI8v7MNtEojrit/mYernaYUSMxhvuQ0QK4skkpkhuhXBI7feH7zA+3vRBUlCOYYtj4cmlBBR771Wm3P3fdQLhHWVZv3v9fnyQgkxtD/eFdIChytlVLi9oI4+zvo7eqws+4zoMedk+XvGTnV+vAkCsN6rDRuX14fdFWaY1vdeni8vlBaUrT6SxLtP1gvkzONsHDPHZcfChcf7yly05G7jSCgbErlbTyg9fmye9fYxG8V96MrNxtLr59MLJYjFLLI6uZZQhmh7/uy+t9TDhWmvSSj3EOI+7505ojbsagz9HkGtLpZM/Ty9UFrQkAQr3GuxPnOlMu8s71UU+N9zYZJQjuHJ5s99HzWw95AGKwQcsyWaPRfCMdHtW7Ux7x/95wgJ5cufv3Rswat+r8X62kv0I45DQWF2Yf1Fv/e1KwnlGNbu+Wi/9/LSvAK/0d9yPcJzszdr2+LFtreFRzLGegd95HEgFwWIpNhaglRePqzCDW5pWF/RPzLTkFCOqZT75TR+B9Zsi8QSNYR6q9ZsTvb69nRCeQ8MEiQSzCsRfR/36N+9JffRi4+EcjRLefajZXjFW1kSyhO8R1dFXG2rNYbomTFEf/Di6Lc/JJQzWTs3FgTR5mXro66qteYbtr0tPJIx1jto1eOimWXPg4eZMVXnBhcX6yP6zAVHQjkzq86NhSX2Pef4/citlnMe9J9t/ew9S0JpkPKWiwC12lWRIdqEObSLWaP1D30suZkXkSWUQ6lKNx5NNNIHOmnQ5mevKQnlHVIoagsk+rj/UqlZ/yr5hZm3hx97n0pCWYndfV+8lQRytVpj6ieMgjFWDRDGnxXIrsqNN6PAk2+2SShZ5B5zXlQ7V7h1JaG8y6nooU6l1xwqCmUkatbX0X34UKHZOCv4M8sHCeUspDvG8cjAvqyG9yttord+lSJEnM0nbKs0CeU/Jiry88+7cT2vNivlaIuc4SesNMZYc2Tk1iMD98WymmcfWGhGuY2whPIfPivVTuYkw7v1AiyqNYafMArG2AxAvD+wAF+zhGwFsityI6H8l/0V+YF30STgn+d8T68HFbsieK+fIDHZJ6s2NSKy9dTbouT3JZT/cKkqlNH994yHLXrhvJhQ4n08m4itnyFmq5DdYsb2yi0SX+yv3KryMzK/o9lqxb/xyvATVhpjbFbyRsvjvT8Eu+UfZpPeO4DAoRrZlbnZwvjoZxLKo4htHx+tmJBPZy4+0Sov89nBdmTHPmXqZ0mhjK6MAODo94kBMRIoEt+MmeoxGvePZojet1rvCAllPifR8huixkwItmrx6J9ty4/Wt8jUz5JCifAjYQMIWAb03ncB0RBDC57tM8nj05O31/qXZ7WeJQllPidbKyfkFYS05+umsBM9WIUd1GfVxtTPskIZfV3OggCycFWDGKLo2g9mnUiILYFsSVORbBtjRf+yfJJQZiH52k6Eq80rTDZQO5gotLrBFvu8vzNqz8XstHei8tqzOb9ZX3tHXFYoEWCPWFpQjvQhpFWbjaOqjxl+RQWN/ZXbCvxsLZmt/0f71UUSeWNj6s2jpYUSQUIst5bhFpTe/pmHQr3AnznOxnHGTvVzJZRjGULt7K2qbK7t9WGr8kyyoWnjaPv2tssLZQsQy2lczSwIR/tYblSfrSBeG1eL/4pbCeV4VnGvEcvpM7WDc2EDtlZoTP1cRigbQVhS7N1DsUCBZCyzVxDIFqP1v+274lZCOY9ViNzR2sFKDhOUVQSyocnUz+WEsoGBLZYBKDZc7e5/sL/n6Z61V6XPEF3F92fw4wr8oHbwIOe+btqD0ZV5ZPi5tFCuTOaW7wzRW/b0WS4C4icXz2xrDD8SymwWJthjiJ7glob4i4D4qZ0KDD8Sytqcut4xRLuGtHMIAuJnCKxpRhl+JJRp8M8zxBA9zzuNJH5q5wDDj4SyNqeudwzRriHtHIKA+BkCa5pRhh8JZRr88wwxRM/zTiOJn9o5wPAjoazNqesdQ7RrSDuHICB+hsCaZpThR0KZBv88QwzR87zTSOKndg4w/Egoa3PqescQ7RrSziEIiJ8hsKYZZfiRUKbBP88QQ/Q87zSS+KmdAww/EsranLreMUS7hrRzCALiZwisaUYZfiSUafDPM8QQPc87jSR+aucAw4+EsjanrncM0a4h7RyCgPgZAmuaUYYfCWUa/PMMMUTP804jiZ/aOcDwI6GszanrHUO0a0g7hyAgfobAmmaU4UdCmQb/PEMM0fO800jip3YOMPxIKGtz6nrHEO0a0s4hCIifIbCmGWX4kVCmwT/PEEP0PO80kvipnQMMPxLK2py63jFEu4a0cwgC4mcIrGlGGX66hNIaVv/l1X9BFB7CQzmwbg70qq+E8mVdklWg4k45cC4HJJQSQM18lQPKgZ0cSBXKXmM6bg4CdhYxZ0SNcgQB8XMErfnHMvx0Lb3nh6IRtxBgiN6yp89yERA/uXhmW2P4kVBmszDBHkP0BLc0xF8ExE/tVGD4kVDW5tT1jiHaNaSdQxAQP0NgTTPK8COhTIN/niGG6HneaSTxUzsHGH4klLU5db1jiHYNaecQBMTPEFjTjDL8SCjT4J9niCF6nncaSfzUzgGGHwllbU5d7xiiXUPaOQQB8TME1jSjDD8SyjT45xliiJ7nnUYSP7VzgOFHQlmbU9c7hmjXkHYOQUD8DIE1zSjDj4QyDf55hhii53mnkcRP7Rxg+JFQ1ubU9Y4h2jWknUMQED9DYE0zyvAjoUyDf54hhuh53mkk8VM7Bxh+JJS1OXW9Y4h2DWnnEATEzxBY04wy/Ego0+CfZ4ghep53Gkn81M4Bhh8JZW1OXe8Yol1D2jkEAfEzBNY0oww/Eso0+OcZYoie551GEj+1c4DhR0JZm1PXO4Zo15B2DkFA/AyBNc0ow4+EMg3+eYYYoud5p5HET+0cYPh5GqH8/v37zf78+vWrNpsb3jFEb5jTR8kIXIkfWzPor1w3jWaGn8sKJUj99OnT7e3bt+E/WHrz5s3tw4cPt69fvy6VAAzRLUlGb4Hl58+fp/+MjuuI/cr87MXx7du328ePHy9ZNy12hp/LCSUE8v3796E4WpBsH6KJAl/himn9buRX2TLY23jYfpX44YeNoZJfW74g91ED1vfePoR1hbpp8du42r697WWEEkSBMAsC08cM9MePH3u4PfRzG9dDHXEGl1CuJZTI9Xfv3p2uG4gsZqMrNKZ+LiGUEMkMshuAIL2yWDY/sa3WJJTrCCVynJ1F2hy0fdx6qd6sv72+hpXGGOsdNPu4PZFEMuBeZLt3hnuXewWNc37+/Jntaoq9ytzs4Wp9z+ynAJtkxMaVZDLdDCYXeyIJLlEzED/MFtHfu3+J2HH7q3Jj+FleKCF6NnDbh4BuLQeQLCDfnmP7SJSKzfpYzb/RD3O8iyIKvlKrzE/Daes2FWpqb5IAniOhxe0r1FbVxvCztFDiymWDtn0kQm/bWoJUXErYOHtjvMJx0SwIhV2pVecHImh9tP0j+Q4+vAsX7H358qUSJa98sfG++mDjl6WFMnr154hINmww87QAtn7FWWXzDdtnatHsf2/2Mxuj6vxEOGL/0RaJLgS0amP4CSuNMTYTGFz5rI+tf4ag6P6aCnEms/5Y0WySuSj6I+TtbbmIbcUW5Tm7XI6W8RVjh08MPyGTjLGZwERkn7mRHM0qqy0jqnMzIg+iWVC1ixhbiCMwi2x6y+UzK6do0lL1zRGmfpYUymi6f4bsllTeDepqsxaG6BbfituVZpPAtzo/1r/WZ5bdLZeiZwVnJi3N9ohtixnb3hYeyRjrHfTscZjhWf9a/8iN6LM+PPL8Fi+2z9BWmk2Cj+r8WP9aX0K5XUlhpTUAsa3WomU3e4+lWnx7/lTmZs/3o5+vNptEfNX58eoH7xmzLbplVfG2CMtPqIKVyba+tX7GsptNlNnntZixvXqLZpNVl3Xgozo/3sMXvEHCNu9d5mrvttrYGH7CSmOMWWdG9XGD2PrW+meWDqN8HWW3xYzt1Zv3Clj1i2J1fqKHL+zFx+Oo2n19WycMP2GlMcasM6P60TQf+5+lVeUmG//sgs72L7JXnZ/odgYE7+jtK282ifhZ0Y0wzdzP8LOcUK64FMskGbYYorN9mGHPm6lUn02uwk/0QBSvDvWKZWSj2jel7nOVqZ/LCGVELpbqEFcU2H3h4T4K9oPYqu983ZO8SiF6fh/Zt+psciV+kPtWNFofdbH1BglqJTr3iNAeyYfMY1uc2Pa28EjGWO+gZ46LCLI2IZq42t0Lo43J6+P4rQSxYzyyb31/pB8jx/a4O/Otq5G+3ttehR/USVRPLQZ8jvuNmEyg7/HSjl1BJMFV8xfb3hYeyRjrHfTMcRGxzSbuVW6RaeOK+hgjmqG2cR65tX4/0o9RY0ezyRUuYsBkNX6w4vK+aGHj2OtXX27bXLWx2P1b/UsJpffagwXlSL/y1dHGsUXuqp95FzrsW6WtyA8mBniX0vre00edVH1fMsoXG1d0zP3+SwglyMKPBcDrY6bYfnquoFXF0sZ2T+jqv68+mwT+K/EDgcSM0rs42Ti2+qgl2Ki8CrN1YWOx+7f6lxBKG7jtQxRReNEVD/v3lh0VlxQ2xi1yV/zMK9iVZpPAfBV+8FDGw9v6f6S/9xCoSj7amHp9uqRQQiAjcfSAwbFbM9Ijtjz72fsYorN9GGHvCrNJ4LICPxHW8B2ChwkC3oW8nyVCXPGgdKteKr9szvJzKaEEweyL50iI6OpabVa5QiEyQurhD05Xa9X5gQBaH20fuX4vjhH+qDXwY89v/Wo1Y2NoPmLb28IjGWO9g545DrNF61vr4wp39l3I6CpbrVhbzNhepUXY49bIaq0yPxDBSNzAwdG2tRpjJy1HfTh6PMNPWGmMsaMOM8dHT+Z6r4J7Y3qzGmBxVoT3xj3yeVVujsRwf6yHOwo6i9f78Ub+Xpmf6M2QMxck1IYnvuC0YmP4WU4oQagNtPWzCMGSodm020pXR+tXVtyPtHOl2SRwrMpPNJvMELSoLivVTctxhp/LCGXWzGOFomWIbklScWkhz9IAAAVkSURBVHul2WRloYRo2dxpfTycOduwBG/27Lbigx3rX2/cywlldCM666+VRPbPLE16yeg9jiG61/bs41bA+ygmVfmJZn1ZteNd8PBMoVpj+FlOKKMrV8ZVEYSuULgM0dWStfkTPZyr9kpW87dnW5Wf6P5k1mos4rIHs5nHMPwsJ5QA1LtxfOZP2VuSJJQWjbH9COuKy7UjSDCFeMQ+e+xoIRttn437/jyGnyWF0nvynfWENLpHmTVjvSeN+Z0hmhln9DlRYa08mwRmVfnx6ga+ZuEd8Tk6j47aZ/hZUigjMcP+sy1anmTdxznrH85niM4YN9PGVWeTlfkZfY/SW+nh/eZqjamfJYVy5GsO3g1pAFupMURX8h++RLOPrNnNI+Otyg9WRda31s/4Fg3epWz27BY8V2vWv17fQgVgjPUOmnFcNPM7s0SOZqpZ9z8z4oaN6tzsxXnl2WRlfiIxy7htNaIe9/KI/Zypn2WFEjMPG7DtM9+iwSw1mk1mLOlZUr3zbKze59X3RbPJSrc3zmBYmZ8ox888QIsufMCh4gqB4WdZoUQiR9+iwRXyqFhGV0QkVrXGEF0lhqioKi7RWMwq8xOtmuAzI5aoM+/eJOxVW4k1Phl+lhbKrVkgwMDN6713xHDFi2Y4sHGVr2C1JHn0NsL6KrNJ4MsU4kxetv5EGj7r4QJ1FT0cQvwQz4qzSZafpYUSQW9d0RphuFLi3iUSoP2A5Oh1iZbozBV2RsI3/7BdqQF763vrX2k2CT5aXFX52asZ+A3BRI1gotBqBlvU0V7d4Pxqt6tsnTD8hJXGGLPOzOxvLSdsHEf6SJS92ejMGO1YNg67v3r/GWaT4GAFfnrE0sZxpA+BrdxsLL1+XkIoEWwm8ZhJVhVJxMoQ3ZsQo46LZpO4IF2trcIPagb4W3/P9LHcrjyTbHlmY2z79raXEUoECnGDyFkgjvSvTPReIoz+PJpNrlBYR7GxOXf03Eccjxlg9EDGxrLVR91VvSd5j6mN4/6z6PdLCWULEoThiXj0KoQFCn0U8UoFa/1vMVfeRrPJim8UZOC4Gj+IGZMM1EDP/ccWH2ajqLNVBLJx2/zHtreFRzLGegedeRxIRKHiqml/kBTYv2K7CjcrYt/j8xX4wbIcD3JszaDf6qbyrak9jhh+Li+Ue6Ct+DlD9Ipxruqz+KnNHMOPhLI2p653DNGuIe0cgoD4GQJrmlGGHwllGvzzDDFEz/NOI4mf2jnA8COhrM2p6x1DtGtIO4cgIH6GwJpmlOFHQpkG/zxDDNHzvNNI4qd2DjD8SChrc+p6xxDtGtLOIQiInyGwphll+JFQpsE/zxBD9DzvNJL4qZ0DDD8Sytqcut4xRLuGtHMIAuJnCKxpRhl+JJRp8M8zxBA9zzuNJH5q5wDDj4SyNqeudwzRriHtHIKA+BkCa5pRhh8JZRr88wwxRM/zTiOJn9o5wPAjoazNqesdQ7RrSDuHICB+hsCaZpThR0KZBv88QwzR87zTSOKndg4w/Egoa3PqescQ7RrSziEIiJ8hsKYZZfiRUKbBP88QQ/Q87zSS+KmdAww/EsranLreMUS7hrRzCALiZwisaUYZfiSUafDPM8QQPc87jSR+aucAw4+EsjanrncM0a4h7RyCgPgZAmuaUYYfCWUa/PMMMUTP804jiZ/aOcDw0yWU1rD6L/R/eRR2wk45UCsHeiVdQvlSizgVkvhQDszLgdNC2WtAxwkBISAEro7A5ozy6sErPiEgBIRADwISyh6UdIwQEAJPjYCE8qnpV/BCQAj0ICCh7EFJxwgBIfDUCEgon5p+BS8EhEAPAhLKHpR0jBAQAk+NwP8AxUiNgha8s58AAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GOAL STATE : "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The H3 heuristic will output 3 for the example state as the 0 is in the wrong column 1 and 2 also. However the true cost is 2 as we just have to switch 0 and 2 , then 2 and 0.\n",
    "\n",
    "H3 using BFS is very similar in terms of performance to BFS H1. However it is less efficient than BFS H2. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "F) A* using heuristics 2 also outperforms A* using H1 . It is also way faster, explores 10x less nodes and find the best solution. \n",
    "\n",
    "In my opinion the second heuristic is better because of the 'entropy' measure of the grid. The manhattan is giving a good idea of how mixed the grid is and is being able to converge rapidly to cycling patterns for the blank tile. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "G) The UCS is better in terms of optimality as it behaves like a Breadth First Search. However if we are looking for speed and memory efficiency we should choose A*. It explores less nodes and founds a solution way faster. It is also quite close in terms of path length. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "BONUSES :\n",
    "\n",
    "-random initial state generator. \n",
    "\n",
    "-function to check if initial state is solvable.(in case a user give an impossible grid configuration)\n",
    "\n",
    "-New heuristic (manhattan distance + linear conflict)\n",
    "\n",
    "\n",
    "We can see through the precedent benchmark that the fourth heuristic that i choose to implement is not outperforming the manhattan distance heuristic. \n",
    "At first glance I thought it would be the case as we add some information about the linear conflict but in the end it does not help to find the best solution. \n",
    "\n",
    "It stills outperforms H1 and H3 as the manhattan distance is included in it..."
   ]
  }
 ],
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