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;
vector<int> v, temp;
int main() {
  int n, elm, prev, ans, j, k;
  int stindex = -1;
  prev = -1;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> elm;
    if (prev > elm) {
      if (stindex == -1) {
        stindex = i;
      }
    }
    v.push_back(elm);
    prev = elm;
  }
  if (stindex == -1) {
    cout << "0";
    return 0;
  }
  ans = n - stindex;
  for (int i = stindex; i < n; ++i) {
    temp.push_back(v[i]);
  }
  j = stindex - 1;
  k = n - 1;
  while (j >= 0) {
    v[k] = v[j];
    --j;
    --k;
  }
  for (int i = 0; i < temp.size(); ++i) v[i] = temp[i];
  prev = -1;
  bool issorted = 1;
  for (int i = 0; i < n; ++i) {
    if (prev > v[i]) {
      issorted = 0;
      break;
    }
    prev = v[i];
  }
  if (issorted) {
    cout << ans;
  } else {
    cout << "-1";
  }
  return 0;
}
