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.
#include <bits/stdc++.h>
template <class T>
inline void read(T &x) {
  x = 0;
  register char c = getchar();
  register bool f = 0;
  while (!isdigit(c)) f ^= c == '-', c = getchar();
  while (isdigit(c)) x = x * 10 + c - '0', c = getchar();
  if (f) x = -x;
}
using namespace std;
int n, m, ans;
string s, t, c, w;
struct node {
  int next, val;
} e[2000006];
int a[1000006];
int main() {
  cin >> n;
  cin >> s;
  cin >> t;
  int rs = 0, rt = 0, flag = 1;
  for (int i = 0; i < n; i++) {
    if (s[i] != t[i]) {
      flag = 0;
      break;
    }
  }
  if (flag) {
    cout << "0" << endl;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (s[i] == '1') {
      rs++;
    }
    if (t[i] == '1') {
      rt++;
    }
  }
  if (rs != rt) {
    cout << "-1" << endl;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (s[i] != t[i]) {
      c += s[i];
      m++;
    }
  }
  while (m > 0) {
    w = "";
    int len = m;
    int i;
    if (c[c.size() - 1] == '1' && c[0] == '0') {
      i = 1;
      m -= 2;
      while (i < c.size() - 1) {
        if (i + 1 >= c.size() - 1) {
          w += c[i];
          break;
        }
        if (c[i] == '1' && c[i + 1] == '0') {
          i += 2;
          m -= 2;
        } else {
          w += c[i];
          i++;
        }
      }
    } else {
      i = 0;
      while (i < c.size()) {
        if (i + 1 >= c.size()) {
          w += c[i];
          break;
        }
        if (c[i] == '1' && c[i + 1] == '0') {
          i += 2;
          m -= 2;
        } else {
          w += c[i];
          i++;
        }
      }
    }
    c = w;
    ans++;
    if (len - 2 == m) {
      ans += m / 2;
      break;
    }
  }
  cout << ans << endl;
  return 0;
}
