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 n, ans = 0, seq[100000];
void read();
void solve();
void write(int ans);
int main() {
  read();
  solve();
  write(ans);
  return 0;
}
void solve() {
  int flag = 0;
  for (int i = 0; i < n - 1; i++) {
    if (seq[i] > seq[i + 1]) {
      flag = i + 1;
      break;
    }
  }
  if (flag == 0)
    ans = 0;
  else {
    bool s = true;
    for (int i = flag; i < n - 1; i++) {
      if (seq[i] > seq[i + 1]) {
        s = false;
        break;
      }
    }
    if (!s)
      ans = -1;
    else {
      if (seq[0] < seq[n - 1])
        ans = -1;
      else
        ans = n - flag;
    }
  }
}
void read() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> seq[i];
}
void write(int ans) { cout << ans << endl; }
