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 from the left of S.
You can repeat the following operation any number of times, possibly zero:

• Choose integers i and j such that $1\leq i < j \leq N. Replace S_i$ with A and S_j with B.

Determine if it is possible to make S equal T. If it is possible, find the minimum number of operations required.

Input

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

Output

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

Constraints

• $2 \leq N \leq 2 \times 10^5$
• Each of S and T is a string of length N consisting of A and B.
• All input numbers are integers.

Sample Input 1

5
BAABA
AABAB

Sample Output 1

2

Performing the operation with i=1 and j=3 changes S to AABBA.
Performing the operation with i=4 and j=5 changes S to AABAB.
Thus, you can make S equal T with two operations. It can be proved that this is the minimum number of operations required, so the answer is 2.

Sample Input 2

2
AB
BA

Sample Output 2

-1

It can be proved that no matter how many operations you perform, you cannot make S equal T.

见题面 Input 部分

见题面 Output 部分