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 oo = 0x3f3f3f3f;
const double eps = 1e-9;
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = (0); i < (n); i++) cin >> a[i];
  int b = -1;
  bool poss = true;
  for (int i = (1); i < (n); i++) {
    if (a[i] < a[i - 1]) {
      if (b == -1) {
        b = i;
      } else
        poss = false;
    }
    if (b != -1) {
      if (a[i] > a[0]) poss = false;
    }
  }
  if (!poss)
    cout << -1 << endl;
  else if (b == -1)
    cout << 0 << endl;
  else
    cout << n - b << endl;
}
