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>
int main() {
  int n, i, k, j, l, z = 0;
  scanf("%d", &n);
  int A[n];
  scanf("%d", &A[0]);
  for (i = 1; i < n; i++) {
    scanf("%d", &A[i]);
    if (A[i] < A[i - 1]) {
      z = 1;
    }
  }
  if (z == 0) {
    printf("0\n");
  } else {
    for (i = 1; i < n; i++) {
      if (A[i] < A[i - 1]) {
        k = 1;
        break;
      }
    }
    for (i = i + 1; i < n; i++) {
      if (A[i] < A[i - 1]) {
        break;
      }
      k++;
    }
    if (i != n) {
      printf("-1\n");
    } else {
      if (A[n - 1] <= A[0]) {
        printf("%d\n", k);
      } else {
        printf("-1\n");
      }
    }
  }
  return 0;
}
