Score : $700$ points

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.

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.

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.

4
AABC
BCAA

YES

This example was explained in the statement.

4
ABCA
BCAB

NO