Problem Statement

You are given two strings $S$ and $T$ of length $N$ consisting of A and B. Let $s_i$ denote the $i$-th character of $S$.

You can perform the following operation on $S$ any number of times, possibly zero:

• Choose an integer pair $(i, j)$ satisfying the following conditions:
• $1 \leq i < j \leq N$
  • $s_i = s_j =$ A
  • $s_{i+1} = s_{i+2} = \ldots = s_{j-1} =$ B
• Then, simultaneously replace each of $s_i, s_{i+1}, \ldots, s_j$ with the other character (A becomes B, and B becomes A).

Determine the minimum number of operations required to make $S$ equal to $T$. If it is impossible, print -1.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $S$ and $T$ are strings of length $N$ consisting of A and B.

Input

The input is given from Standard Input in the following format:

N
S
T

Output

If it is possible to make $S$ equal to $T$, print the minimum number of operations required; otherwise, output -1.