Problem Statement

An electric bulletin board is showing a string $S$ of length $N$ consisting of 0 and 1.

You can do the following operation any number of times, where $S_i$ denotes the $i$-th character $(1 \leq i \leq N)$ of the string shown in the board.

Operation: choose a pair of integers $(l, r)$ $(1 \leq l < r \leq N)$ satisfying one of the conditions below, and swap $S_l$ and $S_r$.

• $S_l=$ 0 and $S_{l+1}=\cdots=S_r=$ 1.
• $S_{l}=\cdots=S_{r-1}=$ 1 and $S_r=$ 0.

Determine whether it is possible to make the string shown in the board match $T$, and find the minimum number of operations needed if it is possible.

Constraints

• $2 \leq N \leq 500000$
• $S$ is a string of length $N$ consisting of 0 and 1.
• $T$ is a string of length $N$ consisting of 0 and 1.

Input

Input is given from Standard Input in the following format:

N
S
T

Output

If it is impossible to make the board show the string $T$, print -1.

If it is possible, find the minimum number of operations needed.