One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

a1, a2, ..., an → an, a1, a2, ..., an - 1.

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer n (2 ≤ n ≤ 105). The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.

Examples

Input

2
2 1


Output

1


Input

3
1 3 2


Output

-1


Input

2
1 2


Output

0
#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 10;
int arr[maxn];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, cnt = 0, res;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> arr[i];
    if (arr[i] >= arr[i - 1])
      cnt++;
    else
      res = i - 1;
  }
  if (cnt == n) {
    cout << 0 << '\n';
    ;
  } else if (cnt < n - 1) {
    cout << -1 << '\n';
    ;
  } else {
    if (arr[n] <= arr[1]) {
      cout << n - res << '\n';
      ;
    } else
      cout << -1 << '\n';
    ;
  }
}
