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 gcd(int xx, int yy) {
  while (yy != 0) {
    xx = xx % yy;
    swap(xx, yy);
  }
  return xx;
}
int lcm(int xx, int yy) { return (xx / gcd(xx, yy)) * yy; }
int a[100005], res, n;
int main() {
  cin >> n;
  for (int i = (1), _b = (n); i <= _b; i++) cin >> a[i];
  int i = n;
  while (i > 1 && a[i] >= a[i - 1]) i--;
  if (i == 1) {
    cout << "0";
    return 0;
  }
  res = n - i + 1;
  if (a[n] > a[1])
    res = -1;
  else {
    int j = 1;
    while (j < n && a[j] <= a[j + 1]) j++;
    if (i != j + 1) res = -1;
  }
  cout << res;
  return 0;
}
