Problem Statement

Given are length-N strings S and T consisting of 0 and 1.
You can do the following operation on S any number of times:

• Choose $i (2 \leq i \leq N)$ such that S_i=1, and replace S_i with 0.
  Additionally, invert S_{i-1}, that is, change it to 1 if it is 0 now and vice versa.

Is it possible to make S exactly match T?
If it is possible, how many operations does it take at least?

Input

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

Output

If it is possible to make S exactly match T, print the minimum number of operations it takes.
Otherwise, print -1.

Constraints

• $1 \leq N \leq 5 \times 10^5$
• S is a string of length N consisting of 0 and 1.
• T is a string of length N consisting of 0 and 1.

Sample Input 1

3
001
100

Sample Output 1

2

We can do as follows: 001 → (choose i=3) → 010 → (choose i=2) → 100.

Sample Input 2

3
001
110

Sample Output 2

-1

Sample Input 3

5
10111
01010

Sample Output 3

5

见题面 Input 部分

见题面 Output 部分