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.*;
import java.math.BigInteger;
import static java.lang.Math.*;

public class Main
{
    static final int mod = (int)1e9+7;
    public static void main(String[] args) throws Exception
    {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int test = 1;
        while(test-- > 0)
        {
            int n = in.nextInt();
            char[] s = in.next().toCharArray();
            char[] t = in.next().toCharArray();
            int c1 = 0, c2 = 0;
            for(int i = 0; i < n; i++) {
                if(s[i] == '1') {
                    c1++;
                }
                if(t[i] == '1') {
                    c2++;
                }
            }
            if(c1 != c2) {
                out.println(-1);
                continue;
            }
            int ans = 0;
            c1 = c2 = 0;
            for(int i = 0; i < n; i++) {
                if(s[i] == t[i]) {
                    continue;
                }
                if(s[i] == '1') {
                    if(c1 == 0)  {
                        ans++;
                        c2++;
                    }
                    else {
                        c1--;
                        c2++;
                    }
                }
                else {
                    if(c2 == 0) {
                        ans++;
                        c1++;
                    }
                    else {
                        c1++;
                        c2--;
                    }
                }
            }
            out.println(ans);
        }
        out.flush();
    }
}

class FastReader
{
    BufferedReader br;
    StringTokenizer st;

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

    public String next() throws IOException
    {
        if(st == null || !st.hasMoreElements())
        {
            st = new StringTokenizer(br.readLine());
        }

        return st.nextToken();
    }

    public boolean hasNext() throws IOException
    {
        if(st != null && st.hasMoreElements())
        {
            return true;
        }

        String s = br.readLine();
        if(s == null) {
            return false;
        }

        st = new StringTokenizer(s);

        return st.hasMoreElements();
    }

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

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

    public String nextLine() throws IOException
    {
        return br.readLine();
    }
}