





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> str:




    """simple docstring"""




    _A     =							0

    # if input_string is "aba" than new_input_string become "a|b|a"
    _A     =							''
    _A     =							''

    # append each character + "|" in new_string for range(0, length-1)
    for i in input_string[: len(_SCREAMING_SNAKE_CASE				) - 1]:
        new_input_string += i + "|"
    # append last character
    new_input_string += input_string[-1]

    # we will store the starting and ending of previous furthest ending palindromic
    # substring
    _A,			_A     =							0, 0

    # length[i] shows the length of palindromic substring with center i
    _A     =							[1 for i in range(len(_SCREAMING_SNAKE_CASE				)				)]

    # for each character in new_string find corresponding palindromic string
    _A     =							0
    for j in range(len(_SCREAMING_SNAKE_CASE				)				):
        _A     =							1 if j > r else min(length[l + r - j] // 2							,     r - j + 1				)
        while (
            j - k >= 0
            and j + k < len(_SCREAMING_SNAKE_CASE				)
            and new_input_string[k + j] == new_input_string[j - k]
        ):
            k += 1

        _A     =							2 * k - 1

        # does this string is ending after the previously explored end (that is r) ?
        # if yes the update the new r to the last index of this
        if j + k - 1 > r:
            _A     =							j - k + 1  # noqa: E741
            _A     =							j + k - 1

        # update max_length and start position
        if max_length < length[j]:
            _A     =							length[j]
            _A     =							j

    # create that string
    _A     =							new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
    for i in s:
        if i != "|":
            output_string += i

    return output_string


if __name__ == "__main__":
 import doctest

 doctest.testmod()









from __future__ import annotations

lowerCAmelCase__			:      Union[str, Any]								=[
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]






def 						a__			(				A__,      A__,      A__,      A__,      A__,      ):
			SCREAMING_SNAKE_CASE_		:     List[Any]					=					[
			    [0 for col in range(len(grid[0]				)				)] for row in range(len(A__				)				)
			]  # the reference grid
			SCREAMING_SNAKE_CASE_		:     List[Any]					=					1
			SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					[
			    [0 for col in range(len(grid[0]				)				)] for row in range(len(A__				)				)
			]  # the action grid

			SCREAMING_SNAKE_CASE_		:     Optional[int]					=					init[0]
			SCREAMING_SNAKE_CASE_		:     List[str]					=					init[1]
			SCREAMING_SNAKE_CASE_		:     Dict					=					0
			SCREAMING_SNAKE_CASE_		:     List[Any]					=					g + heuristic[x][y]  # cost from starting cell to destination cell
			SCREAMING_SNAKE_CASE_		:     List[str]					=					[[f, g, x, y]]

			SCREAMING_SNAKE_CASE_		:     Dict					=					False  # flag that is set when search is complete
			SCREAMING_SNAKE_CASE_		:     Tuple					=					False  # flag set if we can't find expand

			while not found and not resign:
						if len(A__				) == 0:
									raise ValueError('Algorithm is unable to find solution'				)
						else:  # to choose the least costliest action so as to move closer to the goal
									cell.sort()
									cell.reverse()
									SCREAMING_SNAKE_CASE_		:     Any					=					cell.pop()
									SCREAMING_SNAKE_CASE_		:     Any					=					next_cell[2]
									SCREAMING_SNAKE_CASE_		:     str					=					next_cell[3]
									SCREAMING_SNAKE_CASE_		:     Tuple					=					next_cell[1]

									if x == goal[0] and y == goal[1]:
												SCREAMING_SNAKE_CASE_		:     Dict					=					True
									else:
												for i in range(len(A__				)				):  # to try out different valid actions
															SCREAMING_SNAKE_CASE_		:     Optional[int]					=					x + DIRECTIONS[i][0]
															SCREAMING_SNAKE_CASE_		:     List[Any]					=					y + DIRECTIONS[i][1]
															if xa >= 0 and xa < len(A__				) and ya >= 0 and ya < len(grid[0]				):
																		if closed[xa][ya] == 0 and grid[xa][ya] == 0:
																					SCREAMING_SNAKE_CASE_		:     List[Any]					=					g + cost
																					SCREAMING_SNAKE_CASE_		:     List[Any]					=					ga + heuristic[xa][ya]
																					cell.append([fa, ga, xa, ya]				)
																					SCREAMING_SNAKE_CASE_		:     int					=					1
																					SCREAMING_SNAKE_CASE_		:     int					=					i
			SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					[]
			SCREAMING_SNAKE_CASE_		:     List[str]					=					goal[0]
			SCREAMING_SNAKE_CASE_		:     Optional[Any]					=					goal[1]
			invpath.append([x, y]				)  # we get the reverse path from here
			while x != init[0] or y != init[1]:
						SCREAMING_SNAKE_CASE_		:     Any					=					x - DIRECTIONS[action[x][y]][0]
						SCREAMING_SNAKE_CASE_		:     int					=					y - DIRECTIONS[action[x][y]][1]
						SCREAMING_SNAKE_CASE_		:     int					=					xa
						SCREAMING_SNAKE_CASE_		:     List[Any]					=					ya
						invpath.append([x, y]				)

			SCREAMING_SNAKE_CASE_		:     List[Any]					=					[]
			for i in range(len(A__				)				):
						path.append(invpath[len(A__				) - 1 - i]				)
			return path, action


if __name__ == "__main__":
				lowerCAmelCase__			:      Union[str, Any]								=[
				    [0, 1, 0, 0, 0, 0],
				    [0, 1, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
				    [0, 1, 0, 0, 0, 0],
				    [0, 1, 0, 0, 1, 0],
				    [0, 0, 0, 0, 1, 0],
				]

				lowerCAmelCase__			:      Any								=[0, 0]
				# all coordinates are given in format [y,x]
				lowerCAmelCase__			:      List[str]								=[len(grid) - 1, len(grid[0]) - 1]
				lowerCAmelCase__			:      str								=1

				# the cost map which pushes the path closer to the goal
				lowerCAmelCase__			:      Union[str, Any]								=[[0 for row in range(len(grid[0]))] for col in range(len(grid))]
				for i in range(len(grid)):
								for j in range(len(grid[0])):
												lowerCAmelCase__			:      List[str]								=abs(i - goal[0]) + abs(j - goal[1])
												if grid[i][j] == 1:
																# added extra penalty in the heuristic map
																lowerCAmelCase__			:      List[str]								=99

				lowerCAmelCase__							,lowerCAmelCase__			:      Any								=search(grid, init, goal, cost, heuristic)

				print('ACTION MAP')
				for i in range(len(action)):
								print(action[i])

				for i in range(len(path)):
								print(path[i])





