


"""simple docstring"""
def   _a			( )      ->			list[list[int]]:
							return [list(range(1_000 - i			,	-1_000 - i			,	-1			)			) for i in range(1_000			)]


__SCREAMING_SNAKE_CASE							:      Optional[Any]						=      generate_large_matrix()
__SCREAMING_SNAKE_CASE							:      Optional[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   _a			( _SCREAMING_SNAKE_CASE			)      ->			None:
							assert all(row == sorted(_SCREAMING_SNAKE_CASE			,	reverse=_SCREAMING_SNAKE_CASE			) for row in grid			)
							assert all(list(_SCREAMING_SNAKE_CASE			) == sorted(_SCREAMING_SNAKE_CASE			,	reverse=_SCREAMING_SNAKE_CASE			) for col in zip(*_SCREAMING_SNAKE_CASE			)			)







def   _a			( _SCREAMING_SNAKE_CASE			)      ->			int:
							snake_case_          =						0
							snake_case_          =						len(_SCREAMING_SNAKE_CASE			) - 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:
														snake_case_          =						(left + right) // 2
														snake_case_          =						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:
																					snake_case_          =						mid + 1
														else:
																					snake_case_          =						mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
							return len(_SCREAMING_SNAKE_CASE			)







def   _a			( _SCREAMING_SNAKE_CASE			)      ->			int:
							snake_case_          =						0
							snake_case_          =						len(grid[0]			)

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







def   _a			( _SCREAMING_SNAKE_CASE			)      ->			int:
							return len([number for row in grid for number in row if number < 0]			)







def   _a			( _SCREAMING_SNAKE_CASE			)      ->			int:
							snake_case_          =						0
							for row in grid:
														for i, number in enumerate(_SCREAMING_SNAKE_CASE			):
																					if number < 0:
																												total += len(_SCREAMING_SNAKE_CASE			) - i
																												break
							return total







def   _a			( )      ->			None:
							from timeit import timeit

							print("""Running benchmarks"""			)
							snake_case_          =						(
							    """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
							):
														snake_case_          =						timeit(f"""{func}(grid=grid)"""			,	setup=_SCREAMING_SNAKE_CASE			,	number=500			)
														print(f"""{func}() took {time:0.4f} seconds"""			)


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				benchmark()







"""simple docstring"""
from __future__ import annotations

from collections.abc import Iterator





class        __A       :





							'''simple docstring'''

							def __init__(			self							: Any						,    UpperCAmelCase_							: int    )   ->None:



														"""simple docstring"""



														snake_case_          =						value
														snake_case_          =						None
														snake_case_          =						None





class        __A       :





							'''simple docstring'''

							def __init__(			self							: List[Any]						,    UpperCAmelCase_							: Node    )   ->None:



														"""simple docstring"""



														snake_case_          =						tree



							def 						lowerCAmelCase    (			self							: List[str]						,    UpperCAmelCase_							: Node | None    )   ->int:



														"""simple docstring"""



														if node is None:
																					return 0
														return node.value + (
														    self.depth_first_search(node.left    ) + self.depth_first_search(node.right    )
														)



							def __iter__(			self							: str    )   ->Iterator[int]:



														"""simple docstring"""



														yield self.depth_first_search(self.tree    )


if __name__ == "__main__":
				import doctest

				doctest.testmod()



