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;
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  int m = 0;
  while (m < n) {
    cin >> a[m];
    m++;
  }
  int ind = -1;
  for (int i = 0; i < a.size() - 1; i++) {
    if (a[i + 1] < a[i]) {
      ind = i + 1;
      break;
    }
  }
  if (ind == -1) {
    cout << 0 << endl;
  } else {
    vector<int> b(n);
    int j = 0;
    for (int i = ind; i < a.size(); i++) {
      b[j] = a[i];
      j++;
    }
    for (int i = 0; i < ind; i++) {
      b[j] = a[i];
      j++;
    }
    bool sort = true;
    for (int i = 0; i < b.size() - 1; i++) {
      if (b[i + 1] < b[i]) {
        sort = false;
        break;
      }
    }
    if (sort) {
      cout << b.size() - ind << endl;
    } else {
      cout << -1 << endl;
    }
  }
}
