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 PyPy3 (2.4.0) (judge verdict: Accepted)

def is_permutation(s):
    if len(s) == 2 and s[0] != s[1]:
        return False

    mid = int((len(s) - 1) / 2)
    for i in range(mid + 1):
        if s[i] != s[len(s) - 1 - i]:
            return False
    return True

def strong_permutation(s):
    if not is_permutation(s): return False

    last = int((len(s) - 1) / 2)
    s2 = s[:last]
    if not is_permutation(s2): return False

    start = int((len(s) + 3) / 2 - 1)
    s3 = s[start:]
    if not is_permutation(s3): return False

    return True

S = input()
if strong_permutation(S):
    print("Yes")
else:
    print("No")