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.

What is a palindrome? A string $T$ is a palindrome if and only if, for every integer $i$ ($1 \\le i \\le |T|$), the $i$-th character from the beginning and the $i$-th character from the end are the same, where $|T|$ is the length of $T$.

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.

Sample Input 1

3
BBA

Sample Output 1

Yes

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

Sample Input 2

4
ABAB

Sample Output 2

No

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