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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AnandOza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EBinarySubsequenceRotation solver = new EBinarySubsequenceRotation();
        solver.solve(1, in, out);
        out.close();
    }

    static class EBinarySubsequenceRotation {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            char[] sInput = in.next().toCharArray();
            char[] tInput = in.next().toCharArray();
            Util.ASSERT(sInput.length == tInput.length && tInput.length == n);
            int[] s = new int[n];
            for (int i = 0; i < n; i++) {
                s[i] = sInput[i] - '0';
            }
            int[] t = new int[n];
            for (int i = 0; i < n; i++) {
                t[i] = tInput[i] - '0';
            }

            int[] d = new int[n];
            int sum = 0;
            for (int i = 0; i < n; i++) {
                d[i] = t[i] - s[i];
                sum += d[i];
            }

            if (sum != 0) {
                out.println(-1);
                return;
            }

            int pos = 0, neg = 0;

            for (int x : d) {
                if (x == 0)
                    continue;

                if (x > 0) {
                    if (neg == 0)
                        neg++;
                    neg--;
                    pos++;
                } else {
                    if (pos == 0)
                        pos++;
                    pos--;
                    neg++;
                }
            }

            out.println(pos + neg);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }

    static class Util {
        public static void ASSERT(boolean assertion) {
            if (!assertion)
                throw new AssertionError();
        }

        private Util() {
        }

    }
}

