Problem:
Score : 200 points

Problem Statement

A string S of an odd length is said to be a strong palindrome if and only if all of the following conditions are satisfied:

S is a palindrome.

Let N be the length of S. The string formed by the 1-st through ((N-1)/2)-th characters of S is a palindrome.

The string consisting of the (N+3)/2-st through N-th characters of S is a palindrome.

Determine whether S is a strong palindrome.

Constraints

S consists of lowercase English letters.

The length of S is an odd number between 3 and 99 (inclusive).

Input

Input is given from Standard Input in the following format:

S

Output

If S is a strong palindrome, print Yes;
otherwise, print No.

Sample Input 1

akasaka

Sample Output 1

Yes

S is akasaka.

The string formed by the 1-st through the 3-rd characters is aka.

The string formed by the 5-th through the 7-th characters is aka.
All of these are palindromes, so S is a strong palindrome.

Sample Input 2

level

Sample Output 2

No

Sample Input 3

atcoder

Sample Output 3

No

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let is_palindrome s =
  let n = String.length s in
  Array.fold_left ( && ) true @@
  Array.init (n / 2) @@ fun i -> s.[i] = s.[n - i - 1]

let () =
  let s = read_line () in
  let n = String.length s in
  print_endline @@
  if
    is_palindrome s &&
    is_palindrome (String.sub s 0 ((n - 1) / 2)) &&
    is_palindrome (String.sub s ((n + 1) / 2) ((n - 1) / 2))
  then "Yes"
  else "No"