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 as[1000000], save[1000000];
int main() {
  int n;
  while (cin >> n) {
    int i, p = 0, dis;
    for (i = 1; i <= n; i++) {
      cin >> as[i];
      if (i != 1 && as[i] < as[i - 1]) {
        p++;
        dis = i;
      }
    }
    if (p == 0)
      printf("0\n");
    else {
      if (p == 1 && as[1] >= as[n])
        printf("%d\n", (n - dis) + 1);
      else
        printf("-1\n");
    }
  }
  return 0;
}
