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;
  while (cin >> n) {
    int a[100001];
    int f = 0;
    int l = 0;
    int t = 0;
    int min = 1000000001;
    for (int i = 0; i < n; ++i) {
      cin >> a[i];
      if (a[i] < min) {
        t = i + 1;
        min = a[i];
      }
    }
    int time = 0;
    for (int i = 1; i < n; ++i) {
      if (a[i] < a[i - 1]) time++;
      if (a[i] < a[i - 1] && a[i] != min) {
        time = 2;
        break;
      }
    }
    if (time > 1)
      cout << "-1" << endl;
    else if (time == 0)
      cout << "0" << endl;
    else {
      if (a[n - 1] == a[0] && a[0] == min) {
        int i = 0;
        for (i = n - 1; i >= 0; --i) {
          if (a[i] != min) break;
        }
        cout << n - i - 1 << endl;
      } else if (a[n - 1] > a[0])
        cout << "-1" << endl;
      else
        cout << n - t + 1 << endl;
    }
  }
  return 0;
}
