Naman has two binary strings s and t of length n (a binary string is a string which only consists of the characters "0" and "1"). He wants to convert s into t using the following operation as few times as possible.

In one operation, he can choose any subsequence of s and rotate it clockwise once.

For example, if s = 1110100, he can choose a subsequence corresponding to indices (1-based) \{2, 6, 7 \} and rotate them clockwise. The resulting string would then be s = 1010110.

A string a is said to be a subsequence of string b if a can be obtained from b by deleting some characters without changing the ordering of the remaining characters.

To perform a clockwise rotation on a sequence c of size k is to perform an operation which sets c_1:=c_k, c_2:=c_1, c_3:=c_2, …, c_k:=c_{k-1} simultaneously.

Determine the minimum number of operations Naman has to perform to convert s into t or say that it is impossible. 

Input

The first line contains a single integer n (1 ≤ n ≤ 10^6) — the length of the strings.

The second line contains the binary string s of length n.

The third line contains the binary string t of length n.

Output

If it is impossible to convert s to t after any number of operations, print -1.

Otherwise, print the minimum number of operations required.

Examples

Input


6
010000
000001


Output


1

Input


10
1111100000
0000011111


Output


5

Input


8
10101010
01010101


Output


1

Input


10
1111100000
1111100001


Output


-1

Note

In the first test, Naman can choose the subsequence corresponding to indices \{2, 6\} and rotate it once to convert s into t.

In the second test, he can rotate the subsequence corresponding to all indices 5 times. It can be proved, that it is the minimum required number of operations.

In the last test, it is impossible to convert s into t.
import java.util.Scanner;

public class r651e {
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		char[] a=scan.next().toCharArray(), b=scan.next().toCharArray();
		int w0=0, w1=0;
		for(int i=0;i<n;i++) {
			if(a[i]=='0'&&b[i]=='1') w0++;
			if(a[i]=='1'&&b[i]=='0') w1++;
		}
		if(w0!=w1) {
			System.out.println(-1);
		}
		else {
			int s0=0, s1=0;
			for(int i=0;i<n;i++) {
				if(a[i]=='0'&&b[i]=='1') {
					//convert s1 sequence to s0 sequence
					if(s1>0) {
						s1--;
					}
					s0++;
				}
				if(a[i]=='1'&&b[i]=='0') {
					//convert s1 sequence to s0 sequence
					if(s0>0) {
						s0--;
					}
					s1++;
				}
			}
			System.out.println(s0+s1);
		}
	}
}