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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