
"""simple docstring"""

from __future__ import annotations

UpperCamelCase			:       Any									=				list[list[int]]

# assigning initial values to the grid
UpperCamelCase			:       List[Any]									=				[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
UpperCamelCase			:       Union[str, Any]									=				[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]






def 							A		(       snake_case   :Matrix       ,      snake_case   :int       ,      snake_case   :int       ,      snake_case   :int	)   ->			str:
 for i in range(9	):
  if grid[row][i] == n or grid[i][column] == n:
   return False

 for i in range(3	):
  for j in range(3	):
   if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
    return False

 return True






def 							A		(       snake_case   :Matrix	)   ->			int:
 for i in range(9	):
  for j in range(9	):
   if grid[i][j] == 0:
    return i, j
 return None






def 							A		(       snake_case   :Matrix	)   ->			List[Any]:
 if location := find_empty_location(_lowerCamelCase	):
  __UpperCamelCase       						= location
 else:
  # If the location is ``None``, then the grid is solved.
  return grid

 for digit in range(1       ,      1_0	):
  if is_safe(_lowerCamelCase       ,      _lowerCamelCase       ,      _lowerCamelCase       ,      _lowerCamelCase	):
   __UpperCamelCase       						= digit

   if sudoku(_lowerCamelCase	) is not None:
    return grid

   __UpperCamelCase       						= 0

 return None






def 							A		(       snake_case   :Matrix	)   ->			Optional[Any]:
 for row in grid:
  for cell in row:
   print(_lowerCamelCase       ,      end=' '	)
  print()


if __name__ == "__main__":
      # make a copy of grid so that you can compare with the unmodified grid
      for example_grid in (initial_grid, no_solution):
            print("\nExample grid:\n" + "=" * 2_0)
            print_solution(example_grid)
            print("\nExample grid solution:")
            UpperCamelCase			:       List[str]									=				sudoku(example_grid)
            if solution is not None:
                  print_solution(solution)
            else:
                  print("Cannot find a solution.")





"""simple docstring"""

def 							A		(       snake_case   :int	)   ->			bool:
 return str(snake_case	) == str(snake_case	)[::-1]






def 							A		(       snake_case   :int	)   ->			int:
 return int(snake_case	) + int(str(snake_case	)[::-1]	)






def 							A		(       snake_case   :int = 1_0_0_0_0	)   ->			int:
 __UpperCamelCase       						= []
 for num in range(1       ,      snake_case	):
  __UpperCamelCase       						= 0
  __UpperCamelCase       						= num
  while iterations < 5_0:
   __UpperCamelCase       						= sum_reverse(snake_case	)
   iterations += 1
   if is_palindrome(snake_case	):
    break
  else:
   lychrel_nums.append(snake_case	)
 return len(snake_case	)


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



