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() {
  int n;
  cin >> n;
  vector<int> v1;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    v1.push_back(x);
  }
  int index = -1;
  for (int i = 0; i < n - 1; i++) {
    if (v1[i] > v1[i + 1]) {
      index = i + 1;
      break;
    }
  }
  if (index == -1) {
    cout << "0";
  } else {
    vector<int> v2;
    for (int i = index; i < n; i++) v2.push_back(v1[i]);
    for (int i = 0; i < index; i++) v2.push_back(v1[i]);
    bool flag = true;
    for (int i = 0; i < n - 1; i++) {
      if (v2[i] > v2[i + 1]) flag = false;
    }
    if (flag)
      cout << n - index;
    else
      cout << "-1";
  }
}
