'''simple docstring'''




from __future__ import annotations

__UpperCAmelCase     							=[
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]






def __lowerCAmelCase (							UpperCamelCase__				,  UpperCamelCase__				,  UpperCamelCase__				,  UpperCamelCase__				,  UpperCamelCase__				,  )	->    tuple[list[list[int]], list[list[int]]]:
    __lowerCamelCase		=  [
        [0 for col in range(len(grid[0]				)				)] for row in range(len(UpperCamelCase__				)				)
    ]  # the reference grid
    __lowerCamelCase		=  1
    __lowerCamelCase		=  [
        [0 for col in range(len(grid[0]				)				)] for row in range(len(UpperCamelCase__				)				)
    ]  # the action grid

    __lowerCamelCase		=  init[0]
    __lowerCamelCase		=  init[1]
    __lowerCamelCase		=  0
    __lowerCamelCase		=  g + heuristic[x][y]  # cost from starting cell to destination cell
    __lowerCamelCase		=  [[f, g, x, y]]

    __lowerCamelCase		=  False  # flag that is set when search is complete
    __lowerCamelCase		=  False  # flag set if we can't find expand

    while not found and not resign:
        if len(UpperCamelCase__				) == 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()
            __lowerCamelCase		=  cell.pop()
            __lowerCamelCase		=  next_cell[2]
            __lowerCamelCase		=  next_cell[3]
            __lowerCamelCase		=  next_cell[1]

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

    __lowerCamelCase		=  []
    for i in range(len(UpperCamelCase__				)				):
        path.append(invpath[len(UpperCamelCase__				) - 1 - i]				)
    return path, action


if __name__ == "__main__":
  __UpperCAmelCase     							=[
      [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],
  ]

  __UpperCAmelCase     							=[0, 0]
  # all coordinates are given in format [y,x]
  __UpperCAmelCase     							=[len(grid) - 1, len(grid[0]) - 1]
  __UpperCAmelCase     							=1

  # the cost map which pushes the path closer to the goal
  __UpperCAmelCase     							=[[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])):
      __UpperCAmelCase     							=abs(i - goal[0]) + abs(j - goal[1])
      if grid[i][j] == 1:
        # added extra penalty in the heuristic map
        __UpperCAmelCase     							=9_9

  __UpperCAmelCase							,       __UpperCAmelCase     							=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])




def 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					int = 10**12				):
     __UpperCamelCase    							=1
     __UpperCamelCase    							=0

     __UpperCamelCase    							=1
     __UpperCamelCase    							=1

     while numerator <= 2 * min_total - 1:
          prev_numerator += 2 * numerator
          numerator += 2 * prev_numerator

          prev_denominator += 2 * denominator
          denominator += 2 * prev_denominator

     return (denominator + 1) // 2


if __name__ == "__main__":
   print(f"""{solution() = }""")





