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.function.Predicate;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
import java.util.Stack;
import java.util.Vector;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author dauom
 */
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 final void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();
      char[] s = in.nextCharArray();
      char[] t = in.nextCharArray();
      if (ArrayCounter.countMatching(t, c -> c == '0')
          != ArrayCounter.countMatching(s, c -> c == '0')) {
        out.println("-1");
        return;
      }

      TreeSet<Integer> o = new TreeSet<>();
      TreeSet<Integer> z = new TreeSet<>();
      for (int i = n - 1; i >= 0; i--) {
        if (s[i] != t[i]) {
          if (s[i] == '0') {
            z.add(i);
          } else {
            o.add(i);
          }
        }
      }

      int ans = 0;
      Stack<Integer> path = new Stack<>();
      for (int i = 0; i < n; i++) {
        if (s[i] != t[i]) {
          ++ans;
          int j = i;
          path.add(j);
          while (true) {
            Integer nxt = null;
            if (s[j] == '0') {
              nxt = o.higher(j);
            } else {
              nxt = z.higher(j);
            }
            if (nxt == null) {
              break;
            }
            path.add(nxt);
            j = nxt;
          }
          if (path.size() % 2 == 1) {
            path.pop();
          }
          while (!path.isEmpty()) {
            j = path.pop();
            if (s[j] == '0') {
              z.remove(j);
            } else {
              o.remove(j);
            }
            s[j] = t[j];
          }
        }
      }

      out.println(ans);
    }
  }

  static class ArrayCounter {
    private ArrayCounter() {
      throw new RuntimeException("DON'T");
    }

    public static int countMatching(char[] arr, Predicate<Character> test, int from, int to) {
      int ret = 0;
      for (int i = from; i <= to; i++) {
        if (test.test(arr[i])) {
          ++ret;
        }
      }
      return ret;
    }

    public static int countMatching(char[] arr, Predicate<Character> test) {
      return countMatching(arr, test, 0, arr.length - 1);
    }
  }

  static final class InputReader {
    private final InputStream stream;
    private final byte[] buf = new byte[1 << 16];
    private int curChar;
    private int numChars;

    public InputReader() {
      this.stream = System.in;
    }

    public InputReader(final InputStream stream) {
      this.stream = stream;
    }

    private final int read() {
      if (this.numChars == -1) {
        throw new UnknownError();
      } else {
        if (this.curChar >= this.numChars) {
          this.curChar = 0;

          try {
            this.numChars = this.stream.read(this.buf);
          } catch (IOException ex) {
            throw new InputMismatchException();
          }

          if (this.numChars <= 0) {
            return -1;
          }
        }

        return this.buf[this.curChar++];
      }
    }

    public final int nextInt() {
      int c;
      for (c = this.read(); isSpaceChar(c); c = this.read()) {}

      byte sgn = 1;
      if (c == 45) { // 45 == '-'
        sgn = -1;
        c = this.read();
      }

      int res = 0;

      while (c >= 48 && c <= 57) { // 48 == '0', 57 == '9'
        res *= 10;
        res += c - 48; // 48 == '0'
        c = this.read();
        if (isSpaceChar(c)) {
          return res * sgn;
        }
      }

      throw new InputMismatchException();
    }

    public final String next() {
      int c;
      while (isSpaceChar(c = this.read())) {}

      StringBuilder result = new StringBuilder();
      result.appendCodePoint(c);

      while (!isSpaceChar(c = this.read())) {
        result.appendCodePoint(c);
      }

      return result.toString();
    }

    private static final boolean isSpaceChar(final int c) {
      return c == 32 || c == 10 || c == 13 || c == 9
          || c == -1; // 32 == ' ', 10 == '\n', 13 == '\r', 9 == '\t'
    }

    public final char[] nextCharArray() {
      return next().toCharArray();
    }
  }
}
