





"""simple docstring"""




def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:float   ,   SCREAMING_SNAKE_CASE		:float   ,   SCREAMING_SNAKE_CASE		:int   )      ->   float:
 if principal <= 0:
  raise Exception("""Principal borrowed must be > 0"""   )
 if rate_per_annum < 0:
  raise Exception("""Rate of interest must be >= 0"""   )
 if years_to_repay <= 0 or not isinstance(SCREAMING_SNAKE_CASE   ,   SCREAMING_SNAKE_CASE   ):
  raise Exception("""Years to repay must be an integer > 0"""   )

 # Yearly rate is divided by 12 to get monthly rate
 __lowerCAmelCase					:	Tuple      =       rate_per_annum / 12

 # Years to repay is multiplied by 12 to get number of payments as payment is monthly
 __lowerCAmelCase					:	Optional[Any]      =       years_to_repay * 12

 return (
     principal
     * rate_per_month
     * (1 + rate_per_month) ** number_of_payments
     / ((1 + rate_per_month) ** number_of_payments - 1)
 )


if __name__ == "__main__":
      import doctest

      doctest.testmod()






def 	_SCREAMING_SNAKE_CASE		(      )      ->   list[list[int]]:
 return [list(range(1_000 - i   ,   -1_000 - i   ,   -1   )   ) for i in range(1_000   )]


_UpperCAmelCase             =							generate_large_matrix()
_UpperCAmelCase             =							(
    [[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 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:list[list[int]]   )      ->   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 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:list[int]   )      ->   int:
 __lowerCAmelCase					:	Optional[int]      =       0
 __lowerCAmelCase					:	Tuple      =       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:
  __lowerCAmelCase					:	Any      =       (left + right) // 2
  __lowerCAmelCase					:	Optional[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					:	Dict      =       mid + 1
  else:
   __lowerCAmelCase					:	str      =       mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
 return len(SCREAMING_SNAKE_CASE   )






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:list[list[int]]   )      ->   int:
 __lowerCAmelCase					:	Any      =       0
 __lowerCAmelCase					:	Union[str, Any]      =       len(grid[0]   )

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






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






def 	_SCREAMING_SNAKE_CASE		(      SCREAMING_SNAKE_CASE		:list[list[int]]   )      ->   int:
 __lowerCAmelCase					:	List[str]      =       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 	_SCREAMING_SNAKE_CASE		(      )      ->   None:
 from timeit import timeit

 print("""Running benchmarks"""   )
 __lowerCAmelCase					:	Tuple      =       (
     """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					:	Optional[int]      =       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()