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;
bool f(int i, int j, vector<int> &a) {
  while (i + 1 <= j) {
    if (a[i] > a[i + 1]) return 0;
    i++;
  }
  return 1;
}
int main() {
  int n;
  while (cin >> n) {
    vector<int> a(n);
    for (int i = 0; i < n; i++) cin >> a[i];
    int p = -1;
    for (int i = 0; i + 1 < n; i++)
      if (a[i] > a[i + 1]) p = i;
    if (p == -1)
      cout << 0 << endl;
    else
      cout << (a[0] >= a[n - 1] && f(0, p, a) && f(p + 1, n - 1, a) ? n - p - 1
                                                                    : -1)
           << endl;
  }
  return 0;
}
