Score : $400$ points

Problem Statement

You are given a string $S$ of length $N$ consisting of A and B.

You can repeat the following operation zero or more times:

• choose a pair of adjacent characters in $S$ and replace them with AB.

Determine whether $S$ can be turned into a palindrome.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $S$ is a string of length $N$ consisting of A and B.

Input

Input is given from Standard Input in the following format:

$N$

$S$

Output

If $S$ can be turned into a palindrome, print Yes; otherwise, print No.

3
BBA

Yes

Replacing the $2$-nd and $3$-rd characters, BA, with AB will turn $S$ into BAB, a palindrome.

4
ABAB

No

No sequence of operations can turn $S$ into a palindrome.