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.

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.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分