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 Mod = 1e9 + 7;
const int inf = 1 << 31;
map<string, int> Map;
map<string, int>::iterator it;
const int N = 100005;
int a[N];
int main() {
  int n;
  int pos;
  int i, j, k;
  while (cin >> n) {
    int sum = 0;
    for (i = 0; i < n; i++) cin >> a[i];
    for (i = 1; i < n; i++) {
      if (a[i] < a[i - 1]) {
        sum++;
        pos = n - i;
      }
    }
    if (sum == 0)
      cout << 0 << endl;
    else if (sum > 1)
      cout << -1 << endl;
    else {
      if (a[n - 1] <= a[0])
        cout << pos << endl;
      else
        cout << -1 << endl;
    }
  }
  return 0;
}
