


'''simple docstring'''
def       a				(      )  ->     list[list[int]]:



					'''simple docstring'''






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


__snake_case											=					generate_large_matrix()
__snake_case											=					(
    [[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				(      __a       )  ->     None:



					'''simple docstring'''






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


def       a				(      __a       )  ->     int:



					'''simple docstring'''






					UpperCamelCase__       :Optional[Any]							 =			0
					UpperCamelCase__       :Tuple							 =			len(__a       ) - 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__       :Optional[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__       :Optional[int]							 =			mid + 1
										else:
															UpperCamelCase__       :int							 =			mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
					return len(__a       )


def       a				(      __a       )  ->     int:



					'''simple docstring'''






					UpperCamelCase__       :Dict							 =			0
					UpperCamelCase__       :Optional[int]							 =			len(grid[0]       )

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


def       a				(      __a       )  ->     int:



					'''simple docstring'''






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


def       a				(      __a       )  ->     int:



					'''simple docstring'''






					UpperCamelCase__       :List[str]							 =			0
					for row in grid:
										for i, number in enumerate(__a       ):
															if number < 0:
																				total += len(__a       ) - i
																				break
					return total


def       a				(      )  ->     None:



					'''simple docstring'''






					from timeit import timeit

					print('''Running benchmarks'''       )
					UpperCamelCase__       :Dict							 =			(
					    '''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__       :Dict							 =			timeit(f'''{func}(grid=grid)'''			, setup=__a			, 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 typing import Any


def       a				(      __a       )  ->     None:



					'''simple docstring'''






					create_state_space_tree(__a			, []			, 0       )


def       a				(      __a			, __a			, __a       )  ->     None:



					'''simple docstring'''






					if index == len(__a       ):
										print(__a       )
										return

					create_state_space_tree(__a			, __a			, index + 1       )
					current_subsequence.append(sequence[index]       )
					create_state_space_tree(__a			, __a			, index + 1       )
					current_subsequence.pop()


if __name__ == "__main__":
		__snake_case											=					[3, 1, 2, 4]
		generate_all_subsequences(seq)

		seq.clear()
		seq.extend(['''A''', '''B''', '''C'''])
		generate_all_subsequences(seq)