




def lowerCamelCase__   (							snake_case_     :  Tuple	,				snake_case_     :  Union[str, Any]	)				->    Optional[int]:
   __snake_case								=       0
   __snake_case								=       len(__lowerCAmelCase	) - 1

   while left <= right:
      # avoid divided by 0 during interpolation
      if sorted_collection[left] == sorted_collection[right]:
         if sorted_collection[left] == item:
            return left
         else:
            return None

      __snake_case								=       left + ((item - sorted_collection[left]) * (right - left)) // (
          sorted_collection[right] - sorted_collection[left]
      )

      # out of range check
      if point < 0 or point >= len(__lowerCAmelCase	):
         return None

      __snake_case								=       sorted_collection[point]
      if current_item == item:
         return point
      else:
         if point < left:
            __snake_case								=       left
            __snake_case								=       point
         elif point > right:
            __snake_case								=       right
            __snake_case								=       point
         else:
            if item < current_item:
               __snake_case								=       point - 1
            else:
               __snake_case								=       point + 1
   return None






def lowerCamelCase__   (							snake_case_     :  Dict	,				snake_case_     :  Any	,				snake_case_     :  Tuple	,				snake_case_     :  Optional[Any]	)				->    Tuple:

   # avoid divided by 0 during interpolation
   if sorted_collection[left] == sorted_collection[right]:
      if sorted_collection[left] == item:
         return left
      else:
         return None

   __snake_case								=       left + ((item - sorted_collection[left]) * (right - left)) // (
       sorted_collection[right] - sorted_collection[left]
   )

   # out of range check
   if point < 0 or point >= len(__lowerCAmelCase	):
      return None

   if sorted_collection[point] == item:
      return point
   elif point < left:
      return interpolation_search_by_recursion(__lowerCAmelCase	,				__lowerCAmelCase	,				__lowerCAmelCase	,				__lowerCAmelCase	)
   elif point > right:
      return interpolation_search_by_recursion(__lowerCAmelCase	,				__lowerCAmelCase	,				__lowerCAmelCase	,				__lowerCAmelCase	)
   else:
      if sorted_collection[point] > item:
         return interpolation_search_by_recursion(
             __lowerCAmelCase	,				__lowerCAmelCase	,				__lowerCAmelCase	,				point - 1	)
      else:
         return interpolation_search_by_recursion(
             __lowerCAmelCase	,				__lowerCAmelCase	,				point + 1	,				__lowerCAmelCase	)






def lowerCamelCase__   (							snake_case_     :  Optional[int]	)				->    Optional[int]:
   if collection != sorted(__lowerCAmelCase	):
      raise ValueError('''Collection must be ascending sorted'''	)
   return True


if __name__ == "__main__":
    import sys
    snake_case_           =      0
    if debug == 1:
        snake_case_           =      [10, 30, 40, 45, 50, 66, 77, 93]
        try:
            __assert_sorted(collection)
        except ValueError:
            sys.exit('Sequence must be ascending sorted to apply interpolation search')
        snake_case_           =      67

    snake_case_           =      interpolation_search(collection, target)
    if result is not None:
        print(F'{target} found at positions: {result}')
    else:
        print('Not found')








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))

