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;
#pragma GCC target("avx2")
#pragma GCC optimization("O2")
#pragma GCC optimization("unroll-loops")
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
const int N = 1000005;
string S, T;
int n;
set<int> g[2];
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(nullptr);
  cin >> n;
  cin >> S;
  cin >> T;
  int o1 = 0, o2 = 0;
  for (char c : S)
    if (c == '1') o1++;
  for (char c : T)
    if (c == '1') o2++;
  if (o1 != o2) {
    cout << "-1\n";
    return 0;
  }
  set<int> st;
  for (int i = 0; i < n; i++) {
    if (S[i] == T[i]) continue;
    if (S[i] == '0') {
      g[0].insert(i);
    } else {
      g[1].insert(i);
    }
    st.insert(i);
  }
  int moves = 0;
  while (st.size() > 0) {
    moves++;
    int pos = *st.begin();
    int id;
    if (g[0].find(pos) != g[0].end())
      id = 0;
    else
      id = 1;
    while (1) {
      st.erase(st.find(pos));
      g[id].erase(g[id].find(pos));
      id = (id + 1) % 2;
      auto it = g[id].upper_bound(pos);
      if (it == g[id].end()) break;
      pos = *it;
    }
  }
  cout << moves << "\n";
}
