
from __future__ import annotations

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





def        _a   (		lowerCamelCase,      lowerCamelCase,      lowerCamelCase,      lowerCamelCase,      lowerCamelCase,      ):
 lowerCamelCase						:      Any							     = [
     [0 for col in range(len(grid[0]				)				)] for row in range(len(__lowerCAmelCase				)				)
 ]  # the reference grid
 lowerCamelCase						:      int							     = 1
 lowerCamelCase						:      Optional[int]							     = [
     [0 for col in range(len(grid[0]				)				)] for row in range(len(__lowerCAmelCase				)				)
 ]  # the action grid

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

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

 while not found and not resign:
  if len(__lowerCAmelCase				) == 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						:      Any							     = cell.pop()
   lowerCamelCase						:      Optional[Any]							     = next_cell[2]
   lowerCamelCase						:      Tuple							     = next_cell[3]
   lowerCamelCase						:      Union[str, Any]							     = next_cell[1]

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

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


if __name__ == "__main__":
      _lowerCamelCase     =[
          [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     =[0, 0]
      # all coordinates are given in format [y,x]
      _lowerCamelCase     =[len(grid) - 1, len(grid[0]) - 1]
      _lowerCamelCase     =1

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

      _lowerCamelCase  ,    _lowerCamelCase     =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])






from functools import reduce

_A  =	(
    "73167176531330624919225119674426574742355349194934"
    "96983520312774506326239578318016984801869478851843"
    "85861560789112949495459501737958331952853208805511"
    "12540698747158523863050715693290963295227443043557"
    "66896648950445244523161731856403098711121722383113"
    "62229893423380308135336276614282806444486645238749"
    "30358907296290491560440772390713810515859307960866"
    "70172427121883998797908792274921901699720888093776"
    "65727333001053367881220235421809751254540594752243"
    "52584907711670556013604839586446706324415722155397"
    "53697817977846174064955149290862569321978468622482"
    "83972241375657056057490261407972968652414535100474"
    "82166370484403199890008895243450658541227588666881"
    "16427171479924442928230863465674813919123162824586"
    "17866458359124566529476545682848912883142607690042"
    "24219022671055626321111109370544217506941658960408"
    "07198403850962455444362981230987879927244284909188"
    "84580156166097919133875499200524063689912560717606"
    "05886116467109405077541002256983155200055935729725"
    "71636269561882670428252483600823257530420752963450"
)






def   lowerCamelCase__							(							__lowerCAmelCase    :    str = N							):




			"""simple docstring"""


			return max(
			    # mypy cannot properly interpret reduce
			    int(reduce(lambda __lowerCAmelCase       ,				__lowerCAmelCase							: str(int(__lowerCAmelCase							) * int(__lowerCAmelCase							)							)       ,				n[i : i + 13]							)							)
			    for i in range(len(__lowerCAmelCase							) - 12							)							)


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



