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 MAXN = 1e5 + 10;
int a[MAXN];
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> a[i];
  int k = 0;
  while (a[k] <= a[(k + 1) % n] && k < n) ++k;
  k += (k == n ? -n : 1);
  for (int i = 0; i < n - 1; ++i)
    if (a[(k + i) % n] > a[(k + i + 1) % n]) return cout << "-1", 0;
  cout << (n - k) % n;
  return 0;
}
