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 MAX = 1e6;
int num[2][2];
int zero[MAX + 5], one[MAX + 5];
char s[MAX + 5], t[MAX + 5];
int main() {
  int n;
  scanf("%d", &n);
  getchar();
  scanf("%s", s + 1);
  scanf("%s", t + 1);
  for (int i = n; i > 0; i--) {
    if (s[i] == '1' && t[i] == '0') one[i] = 1;
    one[i] += one[i + 1];
    if (s[i] == '0' && t[i] == '1') zero[i] = 1;
    zero[i] += zero[i + 1];
  }
  for (int i = 1; i <= n; i++) {
    if (s[i] == '1' && t[i] == '0') {
      if (num[0][1] > 0) {
        num[0][1]--;
        num[1][1]++;
      } else if (num[0][0] > 0 && zero[i] >= num[1][0] + 1) {
        num[0][0]--;
        num[1][0]++;
      } else
        num[1][0]++;
    }
    if (s[i] == '0' && t[i] == '1') {
      if (num[1][0] > 0) {
        num[1][0]--;
        num[0][0]++;
      } else if (num[1][1] > 0 && one[i] >= num[0][1] + 1) {
        num[1][1]--;
        num[0][1]++;
      } else
        num[0][1]++;
    }
  }
  if (num[0][1] || num[1][0])
    printf("-1\n");
  else
    printf("%d\n", num[1][1] + num[0][0]);
  return 0;
}
