
from __future__ import annotations

UpperCAmelCase__		:     int     			=      [
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]






def   lowerCamelCase__							(					a		,		a		,		a		,		a		,		a		,		)      ->   tuple[list[list[int]], list[list[int]]]:
   _A:  Dict					=       [
       [0 for col in range(len(grid[0]      )      )] for row in range(len(a      )      )
   ]  # the reference grid
   _A:  List[Any]					=       1
   _A:  List[Any]					=       [
       [0 for col in range(len(grid[0]      )      )] for row in range(len(a      )      )
   ]  # the action grid

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

   _A:  str					=       False  # flag that is set when search is complete
   _A:  Union[str, Any]					=       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()
         _A:  Optional[int]					=       cell.pop()
         _A:  int					=       next_cell[2]
         _A:  Tuple					=       next_cell[3]
         _A:  List[str]					=       next_cell[1]

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

   _A:  Optional[Any]					=       []
   for i in range(len(a      )      ):
      path.append(invpath[len(a      ) - 1 - i]      )
   return path, action


if __name__ == "__main__":
   UpperCAmelCase__		:     List[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],
   ]

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

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

   UpperCAmelCase__			,UpperCAmelCase__		:     List[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])





import random

from .binary_exp_mod import bin_exp_mod






def   lowerCamelCase__							(					a		,		a=10_00      )      ->   Optional[int]:
   if n < 2:
      return False

   if n % 2 == 0:
      return n == 2

   # this means n is odd
   _A:  List[Any]					=       n - 1
   _A:  Dict					=       0
   while d % 2 == 0:
      d /= 2
      exp += 1

   # n - 1=d*(2**exp)
   _A:  List[str]					=       0
   while count < prec:
      _A:  Optional[int]					=       random.randint(2		,		n - 1      )
      _A:  Union[str, Any]					=       bin_exp_mod(a		,		a		,		a      )
      if b != 1:
         _A:  Optional[Any]					=       True
         for _ in range(a      ):
            if b == n - 1:
               _A:  int					=       False
               break
            _A:  Optional[Any]					=       b * b
            b %= n
         if flag:
            return False
         count += 1
   return True


if __name__ == "__main__":
   UpperCAmelCase__		:     Dict     			=      abs(int(input('Enter bound : ').strip()))
   print('Here\'s the list of primes:')
   print(', '.join(str(i) for i in range(n + 1) if is_prime_big(i)))



