Score : $300$ points

Problem Statement

Given is a string $S$ consisting of lowercase English letters. Determine whether adding some number of a's (possibly zero) at the beginning of $S$ can make it a palindrome.

Here, a string of length $N$, $A=A_1A_2\ldots A_N$, is said to be a palindrome when $A_i=A_{N+1-i}$ for every $1\leq i\leq N$.

Constraints

• $1 \leq \lvert S \rvert \leq 10^6$
• $S$ consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$S$

Output

If adding some number of a's (possibly zero) at the beginning of $S$ can make it a palindrome, print Yes; otherwise, print No.

kasaka

Yes

By adding one a at the beginning of kasaka, we have akasaka, which is a palindrome, so Yes should be printed.

atcoder

No

Adding any number of a's at the beginning of atcoder does not make it a palindrome.

php

Yes

php itself is a palindrome. Adding zero a's at the beginning of $S$ is allowed, so Yes should be printed.