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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$s = trim(fgets(STDIN));

function F_kai($f_s){
	$c = strlen($f_s);
	if($c == 1 || $c % 2 == 0){
		return false;
	}
	$left = substr($f_s, 0, floor($c / 2));
	$right = strrev(substr($f_s, ceil($c / 2)));
	if($left != $right){
		return false;
	}
	return true;
}

$ret = F_kai($s);
if($ret){
	$ret = F_kai(substr($s, 0, floor(strlen($s) / 2)));
	if($ret){
		echo 'Yes';
		exit;
	}
}

echo 'No';
?>