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 a[1000001];
int main() {
  int n, m, i, j;
  int k, x, y;
  while (~scanf("%d", &n)) {
    for (i = 0; i < n; i++) {
      scanf("%d", &a[i]);
    }
    int s = 0, now = 0;
    for (i = 0; i < n - 1; i++) {
      if (a[i] > a[i + 1]) {
        now = i;
        s++;
      }
    }
    if (s == 0) {
      printf("0\n");
      continue;
    } else if (s == 1 && a[0] >= a[n - 1]) {
      printf("%d\n", n - now - 1);
    } else {
      printf("-1\n");
    }
  }
  return 0;
}
