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
    fscanf(STDIN,"%s",$S);
    $N=strlen($S);
    $untile_sign = ($N-1)/2;
    $start_sign = ($N+3)/2;
    $miss_flag = false;
    
	
    $reverse = $untile_sign-1;
    for($i=0;$i<$untile_sign;$i++){
        // echo $S[$i]." ".$S[$reverse];
        if($S[$i] != $S[$reverse]){
            $miss_flag = true;
        }
        $reverse--;
    }

    $index = $start_sign-1;
    $indexN = $N-1;


    for($i=$index;$i<$N;$i++){
        // echo $S[$i]." ".$S[$indexN];
        if($S[$i] != $S[$indexN]){
            $miss_flag = true;
        }
        $indexN--;
    }

    for($i=0;$i<$N;$i++){
        // echo $S[$i]." ".$S[$indexN];
        if($S[$i] != $S[$indexN]){
            $miss_flag = true;
        }
        $indexN--;
    }

    

    if($miss_flag){
        echo "No\n";
    }else{
        echo "Yes\n";
    }