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 E {
    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;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static int[][] rai(int n, int m) {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextInt();
            }
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static long[][] ral(int n, int m) {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                arr[i][j] = s.nextLong();
            }
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

    static int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }

    public static int primeFactors(int n)
    {
        // Print the number of 2s that divide n
        int max=Integer.MIN_VALUE;
        while (n%2==0)
        {
//            System.out.print(2 + " ");
            n /= 2;
            max=Math.max(2,max);
        }

        // n must be odd at this point.  So we can
        // skip one element (Note i = i +2)
        for (int i = 3; i <= Math.sqrt(n); i+= 2)
        {
            // While i divides n, print i and divide n
            while (n%i == 0)
            {
//                System.out.print(i + " ");
                max=Math.max(max,i);
                n /= i;
            }
        }

        // This condition is to handle the case whien
        // n is a prime number greater than 2
        if (n > 2)
            max=Math.max(n,max);
        return max;
    }
    public static void main(String[] args) {
        StringBuilder ans = new StringBuilder();
//        int t = ri();
        int t=1;
        while (t-- > 0) {
            int n=ri();
            char[] a=rs().toCharArray();
            char[] b= rs().toCharArray();
            TreeSet<Integer> z=new TreeSet<>();
            TreeSet<Integer> o=new TreeSet<>();
            for(int i=0;i<n;i++)
            {
                if(a[i]!=b[i])
                {
                    if(a[i]=='0')
                    {
                        z.add(i);
                    }else o.add(i);
                }
            }
            if(z.size()!=o.size())
            {
                ans.append("-1\n");
                continue;
            }

            int count=0;
            while(z.size()!=0)
            {
                TreeSet<Integer> q1=null;
                TreeSet<Integer> q2=null;
                if(z.first()<o.first())
                {
                    q1=z;q2=o;
                }
                else{
                    q2=z;q1=o;
                }
                int pos=-1;
                while(true)
                {

                    Integer val1=q1.higher(pos);
                    if(val1==null)
                    {
                        break;
                    }
                    Integer val2=q2.higher(val1);
                    if(val2==null)
                    {
                        break;
                    }
                    q1.remove(val1);q2.remove(val2);
                    pos=val2;
                }
                count++;
            }
            ans.append(count).append("\n");

        }
        out.print(ans.toString());
        out.flush();

    }
}


