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;
template <typename T>
string toString(T x) {
  if (x == 0) return "0";
  bool negative = x < 0;
  string res;
  while (x) {
    res.push_back('0' + x % 10);
    x /= 10;
  }
  if (negative) res.push_back('-');
  reverse(res.begin(), res.end());
  return res;
}
template <typename T>
T gcd(T a, T b) {
  return a == 0 ? b : gcd(b % a, a);
}
template <typename T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  int mini = 0;
  int minv = a[0];
  for (int i = 1; i < n; i++) {
    if (a[i] < minv) {
      minv = a[i];
      mini = i;
    }
  }
  if (mini == 0) {
    if (is_sorted(a.begin(), a.end())) {
      cout << 0;
      return 0;
    }
    mini++;
    while (mini < n && a[mini] == minv) mini++;
    mini++;
    while (mini < n && a[mini] != minv) mini++;
    if (mini >= n) {
      cout << -1;
      return 0;
    }
  }
  reverse(a.begin(), a.begin() + mini);
  reverse(a.begin() + mini, a.end());
  reverse(a.begin(), a.end());
  if (is_sorted(a.begin(), a.end())) {
    cout << n - mini;
  } else {
    cout << -1;
  }
  return 0;
}
