





'''simple docstring'''

import random

from .binary_exp_mod import bin_exp_mod

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase=1000      )						->					Any:

   '''simple docstring'''







   if n < 2:
      return False

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

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

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


if __name__ == "__main__":
    a        =						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 __future__ import annotations

import bisect

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase = 0							,	__UpperCAmelCase = -1      )						->					int:

   '''simple docstring'''







   if hi < 0:
      __SCREAMING_SNAKE_CASE      							=       len(__UpperCAmelCase      )

   while lo < hi:
      __SCREAMING_SNAKE_CASE      							=       lo + (hi - lo) // 2
      if sorted_collection[mid] < item:
         __SCREAMING_SNAKE_CASE      							=       mid + 1
      else:
         __SCREAMING_SNAKE_CASE      							=       mid

   return lo

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase = 0							,	__UpperCAmelCase = -1      )						->					int:

   '''simple docstring'''







   if hi < 0:
      __SCREAMING_SNAKE_CASE      							=       len(__UpperCAmelCase      )

   while lo < hi:
      __SCREAMING_SNAKE_CASE      							=       lo + (hi - lo) // 2
      if sorted_collection[mid] <= item:
         __SCREAMING_SNAKE_CASE      							=       mid + 1
      else:
         __SCREAMING_SNAKE_CASE      							=       mid

   return lo

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase = 0							,	__UpperCAmelCase = -1      )						->					None:

   '''simple docstring'''







   sorted_collection.insert(bisect_left(__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase      )							,	__UpperCAmelCase      )

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase = 0							,	__UpperCAmelCase = -1      )						->					None:

   '''simple docstring'''







   sorted_collection.insert(bisect_right(__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase      )							,	__UpperCAmelCase      )

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase      )						->					int | None:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       0
   __SCREAMING_SNAKE_CASE      							=       len(__UpperCAmelCase      ) - 1

   while left <= right:
      __SCREAMING_SNAKE_CASE      							=       left + (right - left) // 2
      __SCREAMING_SNAKE_CASE      							=       sorted_collection[midpoint]
      if current_item == item:
         return midpoint
      elif item < current_item:
         __SCREAMING_SNAKE_CASE      							=       midpoint - 1
      else:
         __SCREAMING_SNAKE_CASE      							=       midpoint + 1
   return None

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase      )						->					int | None:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       bisect.bisect_left(__UpperCAmelCase							,	__UpperCAmelCase      )
   if index != len(__UpperCAmelCase      ) and sorted_collection[index] == item:
      return index
   return None

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase      )						->					int | None:

   '''simple docstring'''







   if right < left:
      return None

   __SCREAMING_SNAKE_CASE      							=       left + (right - left) // 2

   if sorted_collection[midpoint] == item:
      return midpoint
   elif sorted_collection[midpoint] > item:
      return binary_search_by_recursion(__UpperCAmelCase							,	__UpperCAmelCase							,	__UpperCAmelCase							,	midpoint - 1      )
   else:
      return binary_search_by_recursion(__UpperCAmelCase							,	__UpperCAmelCase							,	midpoint + 1							,	__UpperCAmelCase      )


if __name__ == "__main__":
    a        =						input("Enter numbers separated by comma:\n").strip()
    a        =						sorted(int(item) for item in user_input.split(","))
    a        =						int(input("Enter a single number to be found in the list:\n"))
    a        =						binary_search(collection, target)
    if result is None:
        print(F'''{target} was not found in {collection}.''')
    else:
        print(F'''{target} was found at position {result} in {collection}.''')





