
"""simple docstring"""

def 		UpperCAmelCase (		):





		'''simple docstring'''


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


_A						=			generate_large_matrix()
_A						=			(
    [[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 		UpperCAmelCase (		a_      ):





		'''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 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


		lowerCamelCase					:      Optional[int]          =   0
		lowerCamelCase					:      Dict          =   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:
				lowerCamelCase					:      List[Any]          =   (left + right) // 2
				lowerCamelCase					:      int          =   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					:      Tuple          =   mid + 1
				else:
						lowerCamelCase					:      Tuple          =   mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
		return len(a_      )
def 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


		lowerCamelCase					:      List[str]          =   0
		lowerCamelCase					:      Union[str, Any]          =   len(grid[0]      )

		for i in range(len(a_      )      ):
				lowerCamelCase					:      Optional[int]          =   find_negative_index(grid[i][:bound]      )
				total += bound
		return (len(a_      ) * len(grid[0]      )) - total
def 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


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





		'''simple docstring'''


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





		'''simple docstring'''


		from timeit import timeit

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

def 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


		return str(a_      ) == str(a_      )[::-1]
def 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


		return int(a_      ) + int(str(a_      )[::-1]      )
def 		UpperCAmelCase (		a_ = 1_0000      ):





		'''simple docstring'''


		lowerCamelCase					:      Optional[Any]          =   []
		for num in range(1,						a_      ):
				lowerCamelCase					:      List[str]          =   0
				lowerCamelCase					:      Union[str, Any]          =   num
				while iterations < 50:
						lowerCamelCase					:      Optional[int]          =   sum_reverse(a_      )
						iterations += 1
						if is_palindrome(a_      ):
								break
				else:
						lychrel_nums.append(a_      )
		return len(a_      )


if __name__ == "__main__":
					print(F"""{solution() = }""")






