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;
bool isSorted(vector<int> v1) {
  for (int i = 1; i < v1.size(); i++)
    if (v1[i] < v1[i - 1]) return false;
  return true;
}
int main() {
  int n;
  cin >> n;
  vector<int> v1(n);
  for (int i = 0; i < n; i++) cin >> v1[i];
  if (isSorted(v1)) {
    cout << 0;
    return 0;
  }
  int mine = *max_element(v1.begin(), v1.end());
  int minel(0);
  for (int i = 0; i < v1.size(); i++) {
    if (v1[i] == mine) {
      if (i == (v1.size() - 1)) {
        minel = 0;
      } else {
        minel = i + 1;
        if (v1[i] != v1[i + 1]) {
          break;
        }
      }
    }
  }
  rotate(v1.begin(), v1.begin() + minel, v1.end());
  if (isSorted(v1)) {
    cout << n - minel;
  } else
    cout << "-1";
  return 0;
}
