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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Main {

    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int n  = sc.nextInt();
        char[] arr = sc.nextLine().toCharArray();
        char[] brr = sc.nextLine().toCharArray();

        int arr0 = 0, arr1 = 0, brr0 = 0, brr1 = 0;
        //List<Integer> idxsUnmatch = new ArrayList<>();

        //List<Character> aUnmatch  = new ArrayList<>();
        //List<Character> bUnmatch  = new ArrayList<>();
        for(int i = 0; i < n; ++i){
            if(arr[i] != brr[i]){
                //idxsUnmatch.add(i);
                //aUnmatch.add(arr[i]);
                //bUnmatch.add(brr[i]);
                if(arr[i] == '1') ++arr1;
                else ++arr0;
                if(brr[i] == '1') ++brr1;
                else ++brr0;
            }
        }
        if(arr0 == brr0 && arr1 == brr1 && arr0 == arr1){

            int endsWithOne = 0;
            int endsWithZero = 0;
            for(int i = 0; i < n; ++i){
                if(arr[i] == '1' && brr[i] == '0'){
                    if(endsWithZero > 0) --endsWithZero;
                    ++endsWithOne;
                }else if(arr[i] == '0' && brr[i] == '1'){
                    if(endsWithOne > 0) --endsWithOne;
                    ++endsWithZero;
                }
            }

            System.out.println(endsWithOne + endsWithZero);
        }else
            System.out.println(-1);
    }


    private static class FastReader {
        private final 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;
        }

        int[] readArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; ++i)
                arr[i] = nextInt();

            return arr;
        }

        long[] readLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; ++i)
                arr[i] = nextLong();

            return arr;
        }

        double[] readDoubleArray(int n) {
            double[] arr = new double[n];
            for (int i = 0; i < n; ++i)
                arr[i] = nextDouble();
            return arr;
        }
    }
}
