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.util.*;


public class ProbE {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{
        ArrayList<Integer> seg = new ArrayList<>();
        public void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();
            String s = in.nextToken();
            String t = in.nextToken();
            int cnt[] = new int[2];
            int pre = -1, count = 0;
            for (int i = 0; i < n; i++){
                int c1 = s.charAt(i) - '0';
                int c2 = t.charAt(i) - '0';
                cnt[c1]++;
                cnt[c2]--;
                if (c1 == 0 && c2 == 1){
                    if (pre == -1){
                        count = 1;
                        pre = 0;
                    }
                    else if (pre == 0){
                        count++;
                    }
                    else{
                        seg.add(-count);
                        pre = 0;
                        count = 1;
                    }
                }
                else if (c1 == 1 && c2 == 0){
                    if (pre == -1){
                        count = 1;
                        pre = 1;
                    }
                    else if  (pre == 1){
                        count++;
                    }
                    else{
                        seg.add(count);
                        pre = 1;
                        count = 1;
                    }
                }
            }
            if (pre == 1){
                seg.add(-count);
            }
            else{
                seg.add(count);
            }
            if(cnt[0] != 0){
                out.println(-1);
            }
            else{
                out.println(Math.max(get(1), get(-1)));
            }
        }

        private int get(int isPositive) {
            int max = 0;
            int cur = 0;
            for (int i = 0; i < seg.size(); i++){
                cur += seg.get(i) * isPositive;
                max = Math.max(max, cur);
                cur = Math.max(0, cur);
            }
            return max;
        }
    }
    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}