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 INF = 11000000;
const int MOD = 100000000;
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < int(n); i++) {
    cin >> a[i];
  }
  vector<int> b = a;
  bool alr = 1;
  for (int i = 0; i < int(n - 1); i++) {
    if (a[i] > a[i + 1]) alr = 0;
  }
  if (alr) {
    cout << 0 << "\n";
    return 0;
  }
  int mini = 1000000;
  for (int i = 0; i < int(n); i++) {
    mini = min(mini, a[i]);
  }
  int pos = 0;
  for (int i = 0; i < int(n); i++) {
    if (i > 0 && a[i] == mini && a[i - 1] > mini) {
      pos = i;
    }
  }
  rotate(a.begin(), a.begin() + pos, a.end());
  bool ok = 1;
  for (int i = 0; i < int(n - 1); i++) {
    if (a[i] > a[i + 1]) ok = 0;
  }
  if (ok) {
    cout << n - pos << "\n";
  } else {
    cout << -1 << "\n";
  }
}
