





'''simple docstring'''


import random

from .binary_exp_mod import bin_exp_mod
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Tuple			,	SCREAMING_SNAKE_CASE_ :			Any=1_000 )							->     Any:

       """simple docstring"""


       if n < 2:
              return False

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

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

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


if __name__ == "__main__":
    a__			:					List[Any]       						=						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)))







'''simple docstring'''

from random import randint
from tempfile import TemporaryFile

import numpy as np







def a_     (    __UpperCAmelCase				,							__UpperCAmelCase				,							__UpperCAmelCase					)				->					int:





			"""simple docstring"""







			snake_case:    int      							=0
			if start < end:
						snake_case:    Tuple      							=randint(__UpperCAmelCase				,							__UpperCAmelCase					)
						snake_case:    Optional[Any]      							=a[end]
						snake_case:    List[Any]      							=a[pivot]
						snake_case:    int      							=temp

						snake_case							,  snake_case:    Optional[int]      							=_in_place_partition(__UpperCAmelCase				,							__UpperCAmelCase				,							__UpperCAmelCase					)
						count += _in_place_quick_sort(__UpperCAmelCase				,							__UpperCAmelCase				,							p - 1					)
						count += _in_place_quick_sort(__UpperCAmelCase				,							p + 1				,							__UpperCAmelCase					)
			return count







def a_     (    __UpperCAmelCase				,							__UpperCAmelCase				,							__UpperCAmelCase					)				->					Optional[int]:





			"""simple docstring"""







			snake_case:    Tuple      							=0
			snake_case:    Tuple      							=randint(__UpperCAmelCase				,							__UpperCAmelCase					)
			snake_case:    List[Any]      							=a[end]
			snake_case:    List[str]      							=a[pivot]
			snake_case:    Dict      							=temp
			snake_case:    Union[str, Any]      							=start - 1
			for index in range(__UpperCAmelCase				,							__UpperCAmelCase					):
						count += 1
						if a[index] < a[end]:  # check if current val is less than pivot value
									snake_case:    Optional[Any]      							=new_pivot_index + 1
									snake_case:    Dict      							=a[new_pivot_index]
									snake_case:    Union[str, Any]      							=a[index]
									snake_case:    List[Any]      							=temp

			snake_case:    Union[str, Any]      							=a[new_pivot_index + 1]
			snake_case:    Tuple      							=a[end]
			snake_case:    Union[str, Any]      							=temp
			return new_pivot_index + 1, count


a							   =				TemporaryFile()
a							   =				100  # 1000 elements are to be sorted


a   ,      a							   =				0, 1  # mean and standard deviation
a							   =				np.random.normal(mu, sigma, p)
np.save(outfile, X)
print('The array is')
print(X)


outfile.seek(0)  # using the same array
a							   =				np.load(outfile)
a							   =				len(M) - 1
a							   =				_in_place_quick_sort(M, 0, r)

print(
    'No of Comparisons for 100 elements selected from a standard normal distribution'
    'is :'
)







print(z)




