

import random

from .binary_exp_mod import bin_exp_mod
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     Optional[int]   ,      SCREAMING_SNAKE_CASE__      :     Optional[int]=1000				)							->				Union[str, Any]:





				'''simple docstring'''






				if n < 2:
								return False

				if n % 2 == 0:
								return n == 2

				# this means n is odd
				A__   				=       n - 1
				A__   				=       0
				while d % 2 == 0:
								d /= 2
								exp += 1

				# n - 1=d*(2**exp)
				A__   				=       0
				while count < prec:
								A__   				=       random.randint(2   ,      n - 1				)
								A__   				=       bin_exp_mod(UpperCAmelCase__   ,      UpperCAmelCase__   ,      UpperCAmelCase__				)
								if b != 1:
												A__   				=       True
												for _ in range(UpperCAmelCase__				):
																if b == n - 1:
																				A__   				=       False
																				break
																A__   				=       b * b
																b %= n
												if flag:
																return False
												count += 1
				return True


if __name__ == "__main__":
					lowercase_			=  abs(int(input("Enter bound : ").strip()))
					print("Here\'s the list of primes:")
					print(", ".join(str(i) for i in range(n + 1) if is_prime_big(i)))




import random
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     list   ,      SCREAMING_SNAKE_CASE__      :     str				)							->				tuple:





    '''simple docstring'''






    A__				,						A__				,						A__   				=       [], [], []
    for element in data:
        if element < pivot:
            less.append(SCREAMING_SNAKE_CASE__				)
        elif element > pivot:
            greater.append(SCREAMING_SNAKE_CASE__				)
        else:
            equal.append(SCREAMING_SNAKE_CASE__				)
    return less, equal, greater

def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     list   ,      SCREAMING_SNAKE_CASE__      :     int				)							->				str:





    '''simple docstring'''






    if index >= len(SCREAMING_SNAKE_CASE__				) or index < 0:
        return None

    A__   				=       items[random.randint(0   ,      len(SCREAMING_SNAKE_CASE__				) - 1				)]
    A__   				=       0
    A__				,						A__				,						A__   				=       _partition(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				)
    A__   				=       len(SCREAMING_SNAKE_CASE__				)
    A__   				=       len(SCREAMING_SNAKE_CASE__				)

    # index is the pivot
    if m <= index < m + count:
        return pivot
    # must be in smaller
    elif m > index:
        return quick_select(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				)
    # must be in larger
    else:
        return quick_select(SCREAMING_SNAKE_CASE__   ,      index - (m + count)				)

