


def    snake_case_     (  snake_case     )  ->				str:
       lowercase__:   Any  			=   0

       # if input_string is "aba" than new_input_string become "a|b|a"
       lowercase__:   Dict  			=   ''
       lowercase__:   List[Any]  			=   ''

       # append each character + "|" in new_string for range(0, length-1)
       for i in input_string[: len(snake_case     ) - 1]:
              new_input_string += i + "|"
       # append last character
       new_input_string += input_string[-1]

       # we will store the starting and ending of previous furthest ending palindromic
       # substring
       lowercase__			,						lowercase__:   List[Any]  			=   0, 0

       # length[i] shows the length of palindromic substring with center i
       lowercase__:   Optional[int]  			=   [1 for i in range(len(snake_case     )     )]

       # for each character in new_string find corresponding palindromic string
       lowercase__:   Union[str, Any]  			=   0
       for j in range(len(snake_case     )     ):
              lowercase__:   int  			=   1 if j > r else min(length[l + r - j] // 2			,							r - j + 1     )
              while (
                  j - k >= 0
                  and j + k < len(snake_case     )
                  and new_input_string[k + j] == new_input_string[j - k]
              ):
                     k += 1

              lowercase__:   Union[str, Any]  			=   2 * k - 1

              # does this string is ending after the previously explored end (that is r) ?
              # if yes the update the new r to the last index of this
              if j + k - 1 > r:
                     lowercase__:   List[Any]  			=   j - k + 1  # noqa: E741
                     lowercase__:   Optional[Any]  			=   j + k - 1

              # update max_length and start position
              if max_length < length[j]:
                     lowercase__:   Tuple  			=   length[j]
                     lowercase__:   Tuple  			=   j

    # create that string
       lowercase__:   int  			=   new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
       for i in s:
              if i != "|":
                     output_string += i

       return output_string


if __name__ == "__main__":
 import doctest

 doctest.testmod()






from __future__ import annotations




def    snake_case_     (  snake_case			,							snake_case     )  ->				bool:
       if len(snake_case     ) == 0:
              return False
       lowercase__:   Any  			=   len(snake_case     ) // 2
       if a_list[midpoint] == item:
              return True
       if item < a_list[midpoint]:
              return binary_search(a_list[:midpoint]			,							snake_case     )
       else:
              return binary_search(a_list[midpoint + 1 :]			,							snake_case     )


if __name__ == "__main__":
 __lowerCAmelCase		       =							input('''Enter numbers separated by comma:\n''').strip()
 __lowerCAmelCase		       =							[int(item.strip()) for item in user_input.split(''',''')]
 __lowerCAmelCase		       =							int(input('''Enter the number to be found in the list:\n''').strip())
 __lowerCAmelCase		       =							'''''' if binary_search(sequence, target) else '''not '''
 print(F'''{target} was {not_str}found in {sequence}''')


