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 long long mx = (1e5) + 1;
const long long mod = 1000000007;
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  int p = 0;
  for (int i = 0; i < n - 1; i++) {
    if (a[i] <= a[i + 1]) {
      continue;
    } else {
      p = 1;
      break;
    }
  }
  if (p == 0) {
    cout << 0 << endl;
  } else {
    int index = 0;
    for (int i = 0; i < n - 1; i++) {
      if (a[i] > a[i + 1]) {
        index = i;
        break;
      }
    }
    int count = (n - 1) - index;
    int x = 0;
    for (int i = index + 1; i < n - 1; i++) {
      if (a[i] <= a[i + 1]) {
        continue;
      } else {
        x = 1;
        break;
      }
    }
    if (x == 0 && a[n - 1] <= a[0]) {
      cout << count << endl;
    } else {
      cout << -1 << endl;
    }
  }
  return 0;
}
