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 n, a = 200000, b, x, y, i, j, m[200005], mas[100005];
int main() {
  cin >> n;
  while (i < n) {
    cin >> m[i];
    mas[i] = m[i];
    if (m[i] <= a) {
      a = m[i];
      b = i;
    }
    i++;
  }
  i = b - 1;
  while (m[i] == m[b]) {
    b--;
    i--;
  }
  i = 0;
  sort(mas, mas + n);
  while (i < n) {
    if (mas[i] != m[i]) {
      break;
    }
    i++;
  }
  if (i == n) {
    cout << 0;
    return 0;
  }
  i = 0;
  while (i < b) {
    m[n + i] = m[i];
    i++;
  }
  while (i < b + n - 1) {
    if (m[i + 1] < m[i]) {
      cout << -1;
      return 0;
    }
    i++;
  }
  if (b == 0) {
    cout << 0;
    return 0;
  }
  cout << n - b;
}
