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 main() {
  int n;
  cin >> n;
  int a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  bool status = true, allsame = true;
  int ep = n - 1, sp = 0, count = 0;
  while (ep > 0 && a[ep] <= a[sp]) {
    ep--;
    sp--;
    if (sp < 0) sp = n - 1;
    if (a[ep] != a[sp]) allsame = false;
    count++;
  }
  int next = (sp == n - 1) ? 0 : sp + 1;
  while (sp != ep) {
    if (a[next] < a[sp]) {
      status = false;
      cout << -1 << endl;
      break;
    }
    sp++;
    sp = sp % n;
    next = (sp == n - 1) ? 0 : sp + 1;
  }
  if (status && !allsame) cout << count << endl;
  if (allsame && status) cout << 0 << endl;
  return 0;
}
