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.io.PrintWriter;
import java.util.Arrays;
import java.util.TreeSet;

public class Task5 {

    public static void main(String[] args) throws IOException {
        new Task5().solve();
    }

    private void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int n = Integer.parseInt(f.readLine());
        char[] seq1 = f.readLine().toCharArray();
        char[] seq2 = f.readLine().toCharArray();

        int numOfOnes1 = 0;
        int numOfOnes2 = 0;
        for (int i = 0; i < n; i++) if (seq1[i] == '1') numOfOnes1++;
        for (int i = 0; i < n; i++) if (seq2[i] == '1') numOfOnes2++;
        if (numOfOnes1 != numOfOnes2) {
            out.println(-1);
        } else {
            TreeSet<Integer> wrongOne = new TreeSet<Integer>();
            TreeSet<Integer> wrongZero = new TreeSet<Integer>();
            int diff = 0;
            for (int i = 0; i < n; i++) {
                if (seq1[i] != seq2[i]) {
                    diff++;
                    if (seq1[i] == '1') {
                        wrongOne.add(i);
                    } else {
                        wrongZero.add(i);
                    }
                }
            }

            int moves = 0;
            while (!wrongZero.isEmpty()) {
                boolean ena = false;
                if (wrongOne.first() < wrongZero.first()) {
                    ena = true;
                }
                Integer start;
                if (ena) {
                    start = wrongOne.first();
                    wrongOne.remove(start);
                } else {
                    start = wrongZero.first();
                    wrongZero.remove(start);
                }
                boolean a = true;
                int startt = start;
                int last = -1;
                while (a) {
                    //System.out.println(start);
                    //System.out.println(start);
                    if (ena) {
                        last = start;
                        start = wrongZero.ceiling(start);
                        if (start == null) {
                            start = last;
                            a = false;
                        } else {
                            wrongZero.remove(start);
                        }
                        ena = !ena;
                    } else {
                        last = start;
                        start = wrongOne.ceiling(start);
                        if (start == null) {
                            start = last;
                            a = false;
                        } else {
                            wrongOne.remove(start);
                        }
                        ena = !ena;
                    }
                }

                if (seq1[startt] == seq1[last]) {
                    if (seq1[last] == '1') {
                        wrongOne.add(last);
                    } else {
                        wrongZero.add(last);
                    }
                }
                moves++;
            }

            out.println(moves);
        }

        out.close();
    }

    private static char otherChar(char c) {
        if (c == '1') return '0';
        return '1';
    }
}