


"""simple docstring"""


def   snake_case						(				_a:     int							)->		List[Any]:
      '''simple docstring'''


      lowerCamelCase__           =		[[0 for _ in range(_a							)] for _ in range(m + 1							)]
      for i in range(m + 1							):
            lowerCamelCase__           =		1

      for n in range(m + 1							):
            for k in range(1		,   _a							):
                  memo[n][k] += memo[n][k - 1]
                  if n - k > 0:
                        memo[n][k] += memo[n - k - 1][k]

      return memo[m][m - 1]


if __name__ == "__main__":
   import sys

   if len(sys.argv) == 1:
      try:
         _snake_case          =							int(input("Enter a number: ").strip())
         print(partition(n))
      except ValueError:
         print("Please enter a number.")
   else:
      try:
         _snake_case          =							int(sys.argv[1])
         print(partition(n))
      except ValueError:
         print("Please pass a number.")






"""simple docstring"""


from __future__ import annotations

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



def   snake_case						(				_a:     list[list[int]]		,   _a:     list[int]		,   _a:     list[int]		,   _a:     int		,   _a:     list[list[int]]		,   )->		tuple[list[list[int]], list[list[int]]]:
      '''simple docstring'''


      lowerCamelCase__           =		[
          [0 for col in range(len(grid[0]							)							)] for row in range(len(_a							)							)
      ]  # the reference grid
      lowerCamelCase__           =		1
      lowerCamelCase__           =		[
          [0 for col in range(len(grid[0]							)							)] for row in range(len(_a							)							)
      ]  # 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(_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()
                  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(_a							)							):  # to try out different valid actions
                              lowerCamelCase__           =		x + DIRECTIONS[i][0]
                              lowerCamelCase__           =		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:
                                          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(_a							)							):
            path.append(invpath[len(_a							) - 1 - i]							)
      return path, action


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

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

   # the cost map which pushes the path closer to the goal
   _snake_case          =							[[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])):
         _snake_case          =							abs(i - goal[0]) + abs(j - goal[1])
         if grid[i][j] == 1:
            # added extra penalty in the heuristic map
            _snake_case          =							99

   _snake_case      ,					_snake_case          =							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])



