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.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class E {
    static Scanner sc = new Scanner(System.in);
    static PrintWriter pw = new PrintWriter(System.out);

    static void solve() {
        int n = sc.nextInt();
        String s = sc.next();
        String t = sc.next();
        char[] s2 = s.toCharArray();
        char[] t2 = t.toCharArray();
        int numones = 0;
        int numonet = 0;
        for (int i = 0; i < n; i ++){
            if (s2[i] == '1'){
                numones += 1;
            }
            if (t2[i] == '1'){
                numonet += 1;
            }
        }
        if (numones != numonet){
            pw.println(-1);
            return;
        }
        //count number of 101010s and 010101s
        int c0 = 0;
        int c1 = 0;
        for (int i = 0; i < n; i ++){
            if (s2[i] != t2[i]){
                if (s2[i] == '1'){
                    c1 += 1;
                    c0 = Math.max(0, c0 - 1);
                } else if (s2[i] == '0'){
                    c0 += 1;
                    c1 = Math.max(0, c1 - 1);
                }
            }
        }
        pw.println(c0 + c1);
    }

    public static void main(String[] args){
        solve();
        pw.close();
    }
}
