Clay has a binary string ~S~ of length ~N~. By definition, a binary string consists only of ~1~s and ~0~s.

Clay is able to perform two operations on the string:

• Bitwise XOR (~\oplus~) a length ~M~ substring with ~X~ (where ~X~ is a binary string of length ~M~)
• Swap two adjacent bits

Both operations have a cost of ~1~ to perform. Given his starting string and a target string, what is the minimum cost needed to convert from the starting string to the target string?

Input Specification

The first line contains ~N~ ~(1 \le N \le 20)~. The second line contains ~S~, a binary string of length ~N~.

The third line contains ~M~ ~(1 \le N \le N)~. The fourth line contains ~X~, a binary string of length ~M~.

The final line of input contains the target string.

Output Specification

Output an integer representing the minimum cost needed to convert from the starting string to the target string, or -1 if the target string is impossible to reach.

Sample Input

5
10110
3
111
01001

Sample Output

2

Explanation

The target string can be created if you XOR the substring from index ~0~ to ~2~ with ~X~ and swap indices ~3~ and ~4~.