






def 			A__							(      ):





 '''simple docstring'''







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


__lowerCamelCase	:		int										=   generate_large_matrix()
__lowerCamelCase	:		Dict										=   (
    [[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  :					list[list[int]]	):





 '''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  :					list[int]	):





 '''simple docstring'''







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







def 			A__							(      _a  :					list[list[int]]	):





 '''simple docstring'''







 snake_case__  :    List[str]							       =0
 snake_case__  :    List[str]							       =len(grid[0]	)

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







def 			A__							(      _a  :					list[list[int]]	):





 '''simple docstring'''







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







def 			A__							(      _a  :					list[list[int]]	):





 '''simple docstring'''







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







def 			A__							(      ):





 '''simple docstring'''







 from timeit import timeit

 print("""Running benchmarks"""	)
 snake_case__  :    List[str]							       =(
     """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__  :    Optional[int]							       =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()













def 			A__							(      _a  :					Optional[Any]		,  _a  :					Tuple		,  _a  :					List[str]=False	):





 '''simple docstring'''







 if isinstance(_a		,  _a	) and isinstance(_a		,  _a	):
  snake_case__  :    int							       =len(set_a.intersection(_a	)	)

  if alternative_union:
   snake_case__  :    int							       =len(_a	) + len(_a	)
  else:
   snake_case__  :    Tuple							       =len(set_a.union(_a	)	)

  return intersection / union

 if isinstance(_a		,  (list, tuple)	) and isinstance(_a		,  (list, tuple)	):
  snake_case__  :    Optional[int]							       =[element for element in set_a if element in set_b]

  if alternative_union:
   snake_case__  :    Optional[Any]							       =len(_a	) + len(_a	)
   return len(_a	) / union
  else:
   snake_case__  :    Dict							       =set_a + [element for element in set_b if element not in set_a]
   return len(_a	) / len(_a	)

  return len(_a	) / len(_a	)
 return None


if __name__ == "__main__":
       __lowerCamelCase	:		List[Any]										=   {"""a""", """b""", """c""", """d""", """e"""}
       __lowerCamelCase	:		Optional[int]										=   {"""c""", """d""", """e""", """f""", """h""", """i"""}
       print(jaccard_similarity(set_a, set_b))





