Score : $1500$ points

Problem Statement

A string, consisting of letters A, B, and C, is called good, if every two consecutive letters are different. For example, strings ABABAB and ABC are good, while ABBA and AABBCC aren't.

You are given two good strings $S$ and $T$ of length $N$. In one operation, you can choose any letter of $S$, and change it to another letter among A, B, and C, so that $S$ remains good.

What's the smallest number of operations needed to transform $S$ into $T$? We can prove that it can always be done in a finite number of operations.

Constraints

• $1\le N \le 5\cdot 10^5$
• $S$ is a good string of length $N$ consisting of A, B, and C
• $T$ is a good 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

Output the smallest number of operations needed to transform $S$ into $T$.

4
CABC
CBAC

6

Here is one possible sequence of operations of length $6$:

CABC $\to$ BABC $\to$ BCBC $\to$ BCAC $\to$ ACAC $\to$ ABAC $\to$ CBAC

It can be shown that $6$ operations are necessary for this case.

10
ABABABABAB
BABABABABA

15