Problem Statement

You are given a string S of length N, consisting of A, B, and C.
You are allowed to perform the following operation any number of times:

• Choose any i with $1 \le i \le N-2$, such that S_iS_{i+1}S_{i+2} is equal to ABC, BCA, or CAB.
  Then, replace the three characters with ABC, BCA, or CAB.

For example, you can perform the following transformations with string AABC:

• AABC $\to$ ABCA $\to$ BCAA

Determine if you can obtain string T from string S with some finite (maybe zero) number of operations above.

Input

Input is given from Standard Input in the following format:
N
S
T

Output

If you can transform S into T with the operations above, output YES, otherwise output NO.
The checker is case-insensitive: you can use either uppercase or lowercase letters.

Constraints

• $3\le N \le 5\cdot 10^5$
• S is a string of length N consisting of A, B, and C.
• T is a string of length N consisting of A, B, and C.

Sample Input 1

4
AABC
BCAA

Sample Output 1

YES

This example was explained in the statement.

Sample Input 2

4
ABCA
BCAB

Sample Output 2

NO

见题面 Input 部分

见题面 Output 部分