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 checkSeq(deque<int> qu) {
  int saveVal = qu.front();
  for (auto &i : qu) {
    if (i < saveVal) return false;
    saveVal = i;
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int sz, op = 0;
  cin >> sz;
  deque<int> qu;
  for (auto i = 0; i < sz; i++) {
    int x;
    cin >> x;
    qu.push_back(x);
  }
  if (checkSeq(qu))
    cout << op;
  else {
    do {
      qu.push_front(qu.back());
      qu.pop_back();
      op++;
    } while (qu.front() >= qu.back());
    if (checkSeq(qu))
      cout << op;
    else
      cout << -1;
  }
  return 0;
}
