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 a[200000];
int main() {
  int n, i, ind;
  cin >> n;
  for (i = 0; i < n; i++) cin >> a[i];
  a[-1] = -200000;
  a[n] = -200000;
  i = 0;
  while (a[i - 1] <= a[i]) i += 1;
  ind = i;
  while (a[i] <= a[i + 1]) i += 1;
  if (ind == n) {
    cout << 0;
    return 0;
  }
  if ((i < n - 1) or (a[n - 1] > a[0])) {
    cout << -1;
    return 0;
  }
  cout << n - ind;
}
