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, m = 10000000, r = 0;
  int a[100005];
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) {
    if (a[i] == m && (a[i] != a[i - 1])) r = i;
    if (a[i] < m) {
      m = a[i];
      r = i;
    }
  }
  int prev = a[n - 1], flag = 0;
  for (int i = r; i < n - 1; i++) {
    if (a[i] > a[i + 1]) {
      flag = 1;
      break;
    }
  }
  for (int i = 0; i < r; i++) {
    if (a[i] < prev) {
      flag = 1;
      break;
    }
    prev = a[i];
  }
  if (n - r == n)
    r = 0;
  else
    r = n - r;
  if (flag == 0)
    cout << r << endl;
  else
    cout << "-1\n";
}
