


'''simple docstring'''






def 		_A			(lowerCAmelCase__					:int			,  lowerCAmelCase__					:int			,  lowerCAmelCase__					:list[list[int]]						)				->					int:




     '''simple docstring'''



     def update_area_of_max_square(lowerCAmelCase__					:int			,  lowerCAmelCase__					:int						) -> int:
          # BASE CASE
          if row >= rows or col >= cols:
               return 0

          _a      =							update_area_of_max_square(lowerCAmelCase__			,  col + 1						)
          _a      =							update_area_of_max_square(row + 1			,  col + 1						)
          _a      =							update_area_of_max_square(row + 1			,  lowerCAmelCase__						)

          if mat[row][col]:
               _a      =							1 + min([right, diagonal, down]						)
               _a      =							max(largest_square_area[0]			,  lowerCAmelCase__						)
               return sub_problem_sol
          else:
               return 0

     _a      =							[0]
     update_area_of_max_square(0			,  0						)
     return largest_square_area[0]






def 		_A			(lowerCAmelCase__					:int			,  lowerCAmelCase__					:int			,  lowerCAmelCase__					:list[list[int]]						)				->					int:




     '''simple docstring'''



     def update_area_of_max_square_using_dp_array(
         lowerCAmelCase__					:int			,  lowerCAmelCase__					:int			,  lowerCAmelCase__					:list[list[int]]						) -> int:
          if row >= rows or col >= cols:
               return 0
          if dp_array[row][col] != -1:
               return dp_array[row][col]

          _a      =							update_area_of_max_square_using_dp_array(lowerCAmelCase__			,  col + 1			,  lowerCAmelCase__						)
          _a      =							update_area_of_max_square_using_dp_array(row + 1			,  col + 1			,  lowerCAmelCase__						)
          _a      =							update_area_of_max_square_using_dp_array(row + 1			,  lowerCAmelCase__			,  lowerCAmelCase__						)

          if mat[row][col]:
               _a      =							1 + min([right, diagonal, down]						)
               _a      =							max(largest_square_area[0]			,  lowerCAmelCase__						)
               _a      =							sub_problem_sol
               return sub_problem_sol
          else:
               return 0

     _a      =							[0]
     _a      =							[[-1] * cols for _ in range(lowerCAmelCase__						)]
     update_area_of_max_square_using_dp_array(0			,  0			,  lowerCAmelCase__						)

     return largest_square_area[0]






def 		_A			(lowerCAmelCase__					:int			,  lowerCAmelCase__					:int			,  lowerCAmelCase__					:list[list[int]]						)				->					int:




     '''simple docstring'''



     _a      =							[[0] * (cols + 1) for _ in range(rows + 1						)]
     _a      =							0
     for row in range(rows - 1			,  -1			,  -1						):
          for col in range(cols - 1			,  -1			,  -1						):
               _a      =							dp_array[row][col + 1]
               _a      =							dp_array[row + 1][col + 1]
               _a      =							dp_array[row + 1][col]

               if mat[row][col] == 1:
                    _a      =							1 + min(lowerCAmelCase__			,  lowerCAmelCase__			,  lowerCAmelCase__						)
                    _a      =							max(dp_array[row][col]			,  lowerCAmelCase__						)
               else:
                    _a      =							0

     return largest_square_area






def 		_A			(lowerCAmelCase__					:int			,  lowerCAmelCase__					:int			,  lowerCAmelCase__					:list[list[int]]						)				->					int:




     '''simple docstring'''



     _a      =							[0] * (cols + 1)
     _a      =							[0] * (cols + 1)
     _a      =							0
     for row in range(rows - 1			,  -1			,  -1						):
          for col in range(cols - 1			,  -1			,  -1						):
               _a      =							current_row[col + 1]
               _a      =							next_row[col + 1]
               _a      =							next_row[col]

               if mat[row][col] == 1:
                    _a      =							1 + min(lowerCAmelCase__			,  lowerCAmelCase__			,  lowerCAmelCase__						)
                    _a      =							max(current_row[col]			,  lowerCAmelCase__						)
               else:
                    _a      =							0
          _a      =							current_row

     return largest_square_area


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))





'''simple docstring'''






def 		_A			(lowerCAmelCase__					:int						)				->					int:




     '''simple docstring'''



     assert (
         isinstance(lowerCAmelCase__			,  lowerCAmelCase__						) and number_of_steps > 0
     ), f'number_of_steps needs to be positive integer, your input {number_of_steps}'
     if number_of_steps == 1:
          return 1
     _a ,				_a      =							1, 1
     for _ in range(number_of_steps - 1						):
          _a ,				_a      =							current + previous, current
     return current


if __name__ == "__main__":
 import doctest

 doctest.testmod()

