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 main() {
  long long n;
  cin >> n;
  long long arr[n], arrs[n];
  for (long long i = 0; i < n; i++) cin >> arr[i];
  for (long long i = 0; i < n; i++) arrs[i] = arr[i];
  long long more = 0;
  bool tof = false;
  sort(arrs, arrs + n);
  for (long long i = 0; i < n; i++)
    if (arr[i] != arrs[i]) tof = true;
  if (!tof) {
    cout << 0 << endl;
    return 0;
  }
  for (long long i = 0; i < n - 1; i++)
    if (arr[i + 1] < arr[i]) more = i;
  long long narr[n], cnt = 0;
  for (long long i = more + 1; i < n; i++) {
    narr[cnt] = arr[i];
    cnt++;
  }
  for (long long i = 0; i <= more; i++) {
    narr[cnt] = arr[i];
    cnt++;
  }
  tof = false;
  for (long long i = 0; i < n; i++)
    if (narr[i] != arrs[i]) tof = true;
  if (!tof) {
    cout << n - more - 1 << endl;
    return 0;
  } else {
    cout << -1 << endl;
  }
  return 0;
}
