import time
import csv
from collections import deque
import heapq
from abc import ABC, abstractmethod


class Cell:
    def __init__(self, x: int, y: int):
        self.x = x
        self.y = y
        self.isWall = False
        self.isStart = False
        self.isExit = False
        self.weight = 1

    def isPassable(self) -> bool:
        return not self.isWall

    def __lt__(self, other):
        return (self.x, self.y) < (other.x, other.y)


class Maze:
    def __init__(self, width: int, height: int):
        self.width = width
        self.height = height
        self.cells = [[Cell(x, y) for y in range(height)] for x in range(width)]
        self.start = None
        self.exit = None

    def getCell(self, x: int, y: int) -> Cell:
        if 0 <= x < self.width and 0 <= y < self.height:
            return self.cells[x][y]
        return None

    def getNeighbors(self, cell: Cell):
        neighbors = []
        directions = [(0, -1), (0, 1), (-1, 0), (1, 0)]
        for dx, dy in directions:
            nx, ny = cell.x + dx, cell.y + dy
            neighbor = self.getCell(nx, ny)
            if neighbor and neighbor.isPassable():
                neighbors.append(neighbor)
        return neighbors


class MazeBuilder(ABC):
    @abstractmethod
    def buildFromStringList(self, lines: list) -> Maze:
        pass


class TextMazeBuilder(MazeBuilder):

    def buildFromStringList(self, lines: list) -> Maze:
        height = len(lines)
        width = len(lines[0]) if height > 0 else 0
        maze = Maze(width, height)

        for y, line in enumerate(lines):
            for x, char in enumerate(line):
                cell = maze.getCell(x, y)
                if char == '#':
                    cell.isWall = True
                elif char == 'S':
                    cell.isStart = True
                    maze.start = cell
                elif char == 'E':
                    cell.isExit = True
                    maze.exit = cell
                elif char == 'W':
                    cell.weight = 3
                elif char == 'D':
                    cell.weight = 2
        return maze


class PathFindingStrategy(ABC):
    def __init__(self):
        self.visited_count = 0

    @abstractmethod
    def findPath(self, maze: Maze, start: Cell, exit: Cell) -> list:
        pass

    def _reconstruct_path(self, came_from: dict, start: Cell, exit: Cell) -> list:
        if exit not in came_from:
            return []
        path = []
        current = exit
        while current != start:
            path.append(current)
            current = came_from[current]
        path.append(start)
        path.reverse()
        return path


class BFSStrategy(PathFindingStrategy):
    def findPath(self, maze: Maze, start: Cell, exit: Cell) -> list:
        self.visited_count = 0
        queue = deque([start])
        came_from = {start: None}

        while queue:
            current = queue.popleft()
            self.visited_count += 1
            if current == exit:
                break
            for neighbor in maze.getNeighbors(current):
                if neighbor not in came_from:
                    queue.append(neighbor)
                    came_from[neighbor] = current
        return self._reconstruct_path(came_from, start, exit)


class DFSStrategy(PathFindingStrategy):
    def findPath(self, maze: Maze, start: Cell, exit: Cell) -> list:
        self.visited_count = 0
        stack = [start]
        came_from = {start: None}

        while stack:
            current = stack.pop()
            self.visited_count += 1
            if current == exit:
                break
            for neighbor in maze.getNeighbors(current):
                if neighbor not in came_from:
                    stack.append(neighbor)
                    came_from[neighbor] = current
        return self._reconstruct_path(came_from, start, exit)


class AStarStrategy(PathFindingStrategy):
    def findPath(self, maze: Maze, start: Cell, exit: Cell) -> list:
        self.visited_count = 0

        def heuristic(a, b):
            return abs(a.x - b.x) + abs(a.y - b.y)

        pq = []
        heapq.heappush(pq, (0, start))
        came_from = {start: None}
        g_score = {start: 0}

        while pq:
            _, current = heapq.heappop(pq)
            self.visited_count += 1
            if current == exit:
                break

            for neighbor in maze.getNeighbors(current):
                tentative_g_score = g_score[current] + neighbor.weight

                if neighbor not in g_score or tentative_g_score < g_score[neighbor]:
                    came_from[neighbor] = current
                    g_score[neighbor] = tentative_g_score
                    f_score = tentative_g_score + heuristic(neighbor, exit)
                    heapq.heappush(pq, (f_score, neighbor))

        return self._reconstruct_path(came_from, start, exit)


class DijkstraStrategy(PathFindingStrategy):

    def findPath(self, maze: Maze, start: Cell, exit: Cell) -> list:
        self.visited_count = 0
        pq = []
        heapq.heappush(pq, (0, start))
        came_from = {start: None}
        g_score = {start: 0}

        while pq:
            current_g, current = heapq.heappop(pq)
            self.visited_count += 1
            if current == exit:
                break

            for neighbor in maze.getNeighbors(current):
                tentative_g_score = g_score[current] + neighbor.weight

                if neighbor not in g_score or tentative_g_score < g_score[neighbor]:
                    came_from[neighbor] = current
                    g_score[neighbor] = tentative_g_score
                    heapq.heappush(pq, (tentative_g_score, neighbor))

        return self._reconstruct_path(came_from, start, exit)