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() {
  long n;
  scanf("%ld\n", &n);
  std::vector<long> array(n, 0);
  for (int p = 0; p < n; p++) {
    scanf("%ld ", &array[p]);
  }
  bool down = 0, possible = 1;
  long moves(0);
  for (int p = 1; p < n; p++) {
    if (array[p - 1] <= array[p]) {
      continue;
    }
    if (down) {
      possible = 0;
      break;
    }
    down = 1;
    moves = n - p;
    if (array[p] > array[0]) {
      possible = 0;
      break;
    }
  }
  if (down && array[n - 1] > array[0]) {
    possible = 0;
  }
  if (!possible) {
    puts("-1");
  } else {
    printf("%ld\n", moves);
  }
  return 0;
}
