


def      __lowerCamelCase		(				):





			'''simple docstring'''




			return [list(range(1000 - i   ,				-1000 - i   ,				-1	)	) for i in range(1000	)]


UpperCAmelCase					:  Any			=						generate_large_matrix()
UpperCAmelCase					:  Any			=						(
    [[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__						:		List[Any]	):





			'''simple docstring'''




			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__						:		List[str]	):





			'''simple docstring'''




			lowerCamelCase  						=   0
			lowerCamelCase  						=   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:
						lowerCamelCase  						=   (left + right) // 2
						lowerCamelCase  						=   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:
									lowerCamelCase  						=   mid + 1
						else:
									lowerCamelCase  						=   mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
			return len(lowerCamelCase__	)






def      __lowerCamelCase		(				lowerCamelCase__						:		Tuple	):





			'''simple docstring'''




			lowerCamelCase  						=   0
			lowerCamelCase  						=   len(grid[0]	)

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






def      __lowerCamelCase		(				lowerCamelCase__						:		Dict	):





			'''simple docstring'''




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






def      __lowerCamelCase		(				lowerCamelCase__						:		List[str]	):





			'''simple docstring'''




			lowerCamelCase  						=   0
			for row in grid:
						for i, number in enumerate(lowerCamelCase__	):
									if number < 0:
												total += len(lowerCamelCase__	) - i
												break
			return total






def      __lowerCamelCase		(				):





			'''simple docstring'''




			from timeit import timeit

			print("""Running benchmarks"""	)
			lowerCamelCase  						=   (
			    """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
			):
						lowerCamelCase  						=   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()


"""simple docstring"""






import functools



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				UpperCAmelCase__             =							len(lowerCamelCase       )
				UpperCAmelCase__             =							len(lowerCamelCase       )

				@functools.cache
				def min_distance(lowerCamelCase					,			lowerCamelCase       ) -> int:
								# if first word index is overflow - delete all from the second word
								if indexa >= len_worda:
												return len_worda - indexa
								# if second word index is overflow - delete all from the first word
								if indexa >= len_worda:
												return len_worda - indexa
								UpperCAmelCase__             =							int(worda[indexa] != worda[indexa]       )  # current letters not identical
								return min(
								    1 + min_distance(indexa + 1					,			lowerCamelCase       )					,			1 + min_distance(lowerCamelCase					,			indexa + 1       )					,			diff + min_distance(indexa + 1					,			indexa + 1       )					,			)

				return min_distance(0					,			0       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



