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;
using ll = long long int;
using ld = long double;
template <typename Arg1>
void debug_out(const char* name, Arg1&& arg1) {
  cerr << name << " = " << arg1 << " ]"
       << "\n";
}
template <typename Arg1, typename... Args>
void debug_out(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " = " << arg1 << ",";
  debug_out(comma + 1, args...);
}
const long long mod = 1e9 + 7;
const long long N = 1e6 + 5, M = 2e5 + 5;
long long n;
string s, t;
void Solve_main() {
  cin >> n >> s >> t;
  if (count((s).begin(), (s).end(), '1') !=
      count((t).begin(), (t).end(), '1')) {
    cout << -1 << '\n';
    return;
  }
  if (s == t) {
    cout << 0 << '\n';
    return;
  }
  long long mx = -2e6, mn = 2e6;
  long long curr = 0;
  for (long long i = (0); i < (n); ++i) {
    if (s[i] != t[i]) {
      if (s[i] == '1')
        curr++;
      else
        curr--;
      mx = max(mx, curr);
      mn = min(mn, curr);
    }
  }
  long long res = abs(mx) + abs(mn);
  cout << res << '\n';
}
int32_t main() {
  cin.tie(0)->sync_with_stdio(0);
  long long tc = 1;
  for (long long i = 1; i <= tc; i++) {
    Solve_main();
  }
  cerr << "[time:" << 1.0 * clock() / CLOCKS_PER_SEC << "s] ";
  return 0;
}
