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.
// package com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class DM5 {
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String[] Args){
        FastReader scan=new FastReader();
        int t=1;
//        t=scan.nextInt();
        while(t-->0){
            int n=scan.nextInt();
            String s=scan.next();
            String c=scan.next();
            int os=0;
            for(int i=0;i<n;i++){
                if(s.charAt(i)=='1'){
                    os++;
                }
                if(c.charAt(i)=='1'){
                    os--;
                }
            }
            if(os!=0){
                out.println(-1);
            }else{
                int[][] nxt=new int[n][2];
                int nz=-1;
                int no=-1;
                for(int i=n-1;i>=0;i--){
                    if(s.charAt(i)!=c.charAt(i)){
                        nxt[i][0]=nz;
                        nxt[i][1]=no;
                        if(s.charAt(i)=='1'){
                            no=i;
                        }else{
                            nz=i;
                        }
                    }
                }
                Set<Integer> set=new HashSet<>();
                int ans=0;
                for(int i=0;i<n;i++){
                    if(s.charAt(i)!=c.charAt(i)){
                        if(!set.contains(i)){
                            ans++;
                            set.add(i);
                            int m=0;
                            if(s.charAt(i)=='0'){
                                m=1;
                            }
                            int ni=i;
                            while((ni=find(nxt,ni,m,set))!=-1){
                                set.add(ni);
                                m=(m+1)%2;
                            }
                        }
                    }
                }
                out.println(ans);
            }
        }
        out.flush();
        out.close();
    }
    static int find(int[][] nxt,int ni,int m,Set<Integer> s){
        if(nxt[ni][m]==-1){
            return -1;
        }
        if(s.contains(nxt[ni][m])){
            return nxt[ni][m]=find(nxt,nxt[ni][m],m,s);
        }else{
            return nxt[ni][m];
        }
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

}
