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.*;
import java.io.*;

public class E {
    public static void main(String[] args) throws IOException{
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(f.readLine());
        String str1 = f.readLine();
        String str2 = f.readLine();
        int z1 = 0;
        int z2 = 0;
        for(int i = 0; i < n; i++){
            if(str1.charAt(i) == '0') z1++;
            if(str2.charAt(i) == '0') z2++;
        }
        if(z1 != z2){
            out.println(-1);
            out.close();
            System.exit(0);
        }
        StringBuilder nstr = new StringBuilder();
        for(int i = 0; i < n; i++){
            if(str1.charAt(i) != str2.charAt(i)) nstr.append(str1.charAt(i));
        }
        String str3 = nstr.toString();
        int cnt = 0;
        LinkedList<Integer> zeros = new LinkedList<Integer>();
        LinkedList<Integer> ones = new LinkedList<Integer>();
        for(int i = 0; i < str3.length(); i++){
            if(str3.charAt(i) == '0'){
                if(!ones.isEmpty()){
                    zeros.add(ones.remove());
                }else{
                    cnt++;
                    zeros.add(cnt);
                }
            }else{
                if(!zeros.isEmpty()){
                    ones.add(zeros.remove());
                }else{
                    cnt++;
                    ones.add(cnt);
                }
            }
        }
        out.println(cnt);


        out.close();
    }
}
