






import sys

__a:     str   					=					(
    '''73167176531330624919225119674426574742355349194934'''
    '''96983520312774506326239578318016984801869478851843'''
    '''85861560789112949495459501737958331952853208805511'''
    '''12540698747158523863050715693290963295227443043557'''
    '''66896648950445244523161731856403098711121722383113'''
    '''62229893423380308135336276614282806444486645238749'''
    '''30358907296290491560440772390713810515859307960866'''
    '''70172427121883998797908792274921901699720888093776'''
    '''65727333001053367881220235421809751254540594752243'''
    '''52584907711670556013604839586446706324415722155397'''
    '''53697817977846174064955149290862569321978468622482'''
    '''83972241375657056057490261407972968652414535100474'''
    '''82166370484403199890008895243450658541227588666881'''
    '''16427171479924442928230863465674813919123162824586'''
    '''17866458359124566529476545682848912883142607690042'''
    '''24219022671055626321111109370544217506941658960408'''
    '''07198403850962455444362981230987879927244284909188'''
    '''84580156166097919133875499200524063689912560717606'''
    '''05886116467109405077541002256983155200055935729725'''
    '''71636269561882670428252483600823257530420752963450'''
)




def       _SCREAMING_SNAKE_CASE (							__snake_case = N )				->						int:
       _UpperCAmelCase							=    -sys.maxsize - 1
       for i in range(len(__snake_case ) - 1_2 ):
              _UpperCAmelCase							=    1
              for j in range(1_3 ):
                     product *= int(n[i + j] )
              if product > largest_product:
                     _UpperCAmelCase							=    product
       return largest_product


if __name__ == "__main__":
  print(F"{solution() = }")


"""simple docstring"""


def   _A					(	_a	:						Optional[int]     ,   _a	:						str				):



      """simple docstring"""






      A				  =		0
      A				  =		len(_a				) - 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

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

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

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



def   _A					(	_a	:						Any     ,   _a	:						List[str]     ,   _a	:						Dict     ,   _a	:						List[str]				):



      """simple docstring"""






      if sorted_collection[left] == sorted_collection[right]:
            if sorted_collection[left] == item:
                  return left
            else:
                  return None

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

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

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



def   _A					(	_a	:						List[Any]				):



      """simple docstring"""






      if collection != sorted(_a				):
            raise ValueError("""Collection must be ascending sorted"""				)
      return True


if __name__ == "__main__":
  import sys
  UpperCAmelCase													=0
  if debug == 1:
    UpperCAmelCase													=[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")
    UpperCAmelCase													=67

  UpperCAmelCase													=interpolation_search(collection, target)
  if result is not None:
    print(f"""{target} found at positions: {result}""")
  else:
    print("Not found")




