


"""simple docstring"""


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




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

						__lowerCAmelCase				    =			update_area_of_max_square(_UpperCamelCase    , col + 1      )
						__lowerCAmelCase				    =			update_area_of_max_square(row + 1    , col + 1      )
						__lowerCAmelCase				    =			update_area_of_max_square(row + 1    , _UpperCamelCase      )

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

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


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




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

						__lowerCAmelCase				    =			update_area_of_max_square_using_dp_array(_UpperCamelCase    , col + 1    , _UpperCamelCase      )
						__lowerCAmelCase				    =			update_area_of_max_square_using_dp_array(row + 1    , col + 1    , _UpperCamelCase      )
						__lowerCAmelCase				    =			update_area_of_max_square_using_dp_array(row + 1    , _UpperCamelCase    , _UpperCamelCase      )

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

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

			return largest_square_area[0]


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




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

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

			return largest_square_area


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




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

									if mat[row][col] == 1:
												__lowerCAmelCase				    =			1 + min(_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      )
												__lowerCAmelCase				    =			max(current_row[col]    , _UpperCamelCase      )
									else:
												__lowerCAmelCase				    =			0
						__lowerCAmelCase				    =			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        __lowerCAmelCase       ():
		return [list(range(1_000 - i					,       -1_000 - i					,       -1      )      ) for i in range(1_000      )]


lowerCamelCase__					=   generate_large_matrix()
lowerCamelCase__					=   (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		assert all(row == sorted(__lowerCAmelCase					,       reverse=__lowerCAmelCase      ) for row in grid      )
		assert all(list(__lowerCAmelCase      ) == sorted(__lowerCAmelCase					,       reverse=__lowerCAmelCase      ) for col in zip(*__lowerCAmelCase      )      )






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		_UpperCAmelCase						:				Any	    =					0
		_UpperCAmelCase						:				str	    =					len(__lowerCAmelCase      ) - 1

		# Edge cases such as no values or all numbers are negative.
		if not array or array[0] < 0:
				return 0

		while right + 1 > left:
				_UpperCAmelCase						:				Union[str, Any]	    =					(left + right) // 2
				_UpperCAmelCase						:				List[str]	    =					array[mid]

				# Num must be negative and the index must be greater than or equal to 0.
				if num < 0 and array[mid - 1] >= 0:
						return mid

				if num >= 0:
						_UpperCAmelCase						:				Tuple	    =					mid + 1
				else:
						_UpperCAmelCase						:				Optional[Any]	    =					mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
		return len(__lowerCAmelCase      )






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		_UpperCAmelCase						:				str	    =					0
		_UpperCAmelCase						:				int	    =					len(grid[0]      )

		for i in range(len(__lowerCAmelCase      )      ):
				_UpperCAmelCase						:				Dict	    =					find_negative_index(grid[i][:bound]      )
				total += bound
		return (len(__lowerCAmelCase      ) * len(grid[0]      )) - total






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		return len([number for row in grid for number in row if number < 0]      )






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		_UpperCAmelCase						:				Tuple	    =					0
		for row in grid:
				for i, number in enumerate(__lowerCAmelCase      ):
						if number < 0:
								total += len(__lowerCAmelCase      ) - i
								break
		return total






def        __lowerCAmelCase       ():
		from timeit import timeit

		print("Running benchmarks"      )
		_UpperCAmelCase						:				Tuple	    =					(
		    "from __main__ import count_negatives_binary_search, "
		    "count_negatives_brute_force, count_negatives_brute_force_with_break, grid"
		)
		for func in (
		    "count_negatives_binary_search",  # took 0.7727 seconds
		    "count_negatives_brute_force_with_break",  # took 4.6505 seconds
		    "count_negatives_brute_force",  # took 12.8160 seconds
		):
				_UpperCAmelCase						:				str	    =					timeit(F"""{func}(grid=grid)"""					,       setup=__lowerCAmelCase					,       number=500      )
				print(F"""{func}() took {time:0.4f} seconds"""      )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						benchmark()



