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 long long inf = 1e6;
const long long MOD = 1e9 + 7;
const long long N = 1e6 + 7;
const long long N_N = 1e3;
const int INF = 1e9 + 228;
const long double eps = 1e-12;
long long n, a[N], ans, l, ans1;
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
  }
  for (int i = 2; i <= n; ++i) {
    if (a[i - 1] > a[i]) {
      ans++;
      ans1 = i;
    }
  }
  if (ans > 1) {
    cout << -1;
  }
  if (ans == 0) {
    cout << 0;
  }
  if (ans == 1) {
    if (a[1] >= a[ans1] && a[1] >= a[n]) {
      cout << n - ans1 + 1;
    } else
      cout << -1;
  }
  return 0;
}
