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>
using namespace std;
const int_fast32_t inf = 1e9 + 7;
const int_fast32_t MOD = 1000000007;
const int_fast64_t llinf = 1e18;
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int_fast32_t n;
  cin >> n;
  string s, t;
  cin >> s >> t;
  {
    int_fast32_t cnt = 0;
    for (int_fast64_t i = 0; i < (n); ++i) cnt += s[i] - '0';
    for (int_fast64_t i = 0; i < (n); ++i) cnt -= t[i] - '0';
    if (cnt != 0) {
      cout << (-1) << "\n";
      return 0;
    }
  }
  int_fast32_t ans = 0;
  int_fast32_t cnt[2] = {0, 0};
  for (int_fast64_t i = 0; i < (n); ++i) {
    if (s[i] == t[i]) continue;
    if (s[i] == '0') {
      if (cnt[1] > 0) {
        cnt[1]--;
        cnt[0]++;
      } else {
        cnt[0]++;
        ans++;
      }
    } else {
      if (cnt[0] > 0) {
        cnt[0]--;
        cnt[1]++;
      } else {
        cnt[1]++;
        ans++;
      }
    }
  }
  cout << (ans) << "\n";
  return 0;
}
