





def lowerCamelCase__   (							)				->    list[list[int]]:
   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 lowerCamelCase__   (							snake_case_     :  list[list[int]]	)				->    None:
   assert all(row == sorted(snake_case_	,				reverse=snake_case_	) for row in grid	)
   assert all(list(snake_case_	) == sorted(snake_case_	,				reverse=snake_case_	) for col in zip(*snake_case_	)	)






def lowerCamelCase__   (							snake_case_     :  list[int]	)				->    int:
   __snake_case								=       0
   __snake_case								=       len(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(snake_case_	)






def lowerCamelCase__   (							snake_case_     :  list[list[int]]	)				->    int:
   __snake_case								=       0
   __snake_case								=       len(grid[0]	)

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






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






def lowerCamelCase__   (							snake_case_     :  list[list[int]]	)				->    int:
   __snake_case								=       0
   for row in grid:
      for i, number in enumerate(snake_case_	):
         if number < 0:
            total += len(snake_case_	) - i
            break
   return total






def lowerCamelCase__   (							)				->    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=snake_case_	,				number=500	)
      print(f"""{func}() took {time:0.4f} seconds"""	)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    benchmark()








import math






def lowerCamelCase__   (							snake_case_     :  int	)				->    list[int]:
   __snake_case								=       []
   __snake_case								=       2
   __snake_case								=       int(math.sqrt(snake_case_	)	)  # Size of every segment
   __snake_case								=       [True] * (end + 1)
   __snake_case								=       []

   while start <= end:
      if temp[start] is True:
         in_prime.append(snake_case_	)
         for i in range(start * start	,				end + 1	,				snake_case_	):
            __snake_case								=       False
      start += 1
   prime += in_prime

   __snake_case								=       end + 1
   __snake_case								=       min(2 * end	,				snake_case_	)

   while low <= n:
      __snake_case								=       [True] * (high - low + 1)
      for each in in_prime:
         __snake_case								=       math.floor(low / each	) * each
         if t < low:
            t += each

         for j in range(snake_case_	,				high + 1	,				snake_case_	):
            __snake_case								=       False

      for j in range(len(snake_case_	)	):
         if temp[j] is True:
            prime.append(j + low	)

      __snake_case								=       high + 1
      __snake_case								=       min(high + end	,				snake_case_	)

   return prime







print(sieve(10**6))

