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;
  cin >> n;
  deque<int> a;
  int count = 0;
  for (int i = 0; i < n; i++) {
    int temp;
    cin >> temp;
    a.push_back(temp);
  }
  bool flag = true;
  for (int i = 1; i < n; i++) {
    if (a[i] == a[i - 1]) {
      continue;
    } else {
      flag = false;
      break;
    }
  }
  if (flag == true) {
    cout << "0";
  } else {
    flag = true;
    int c = n - 1;
    while (c--) {
      if (a[n - 1] <= a[0]) {
        int temp = a[n - 1];
        a.pop_back();
        a.push_front(temp);
        count++;
      } else {
        break;
      }
    }
    for (int i = 1; i < n; i++) {
      if (a[i] >= a[i - 1]) {
        continue;
      } else {
        flag = false;
        break;
      }
    }
    if (flag == true) {
      cout << count;
    } else {
      cout << "-1";
    }
  }
}
