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;
const int maxn = 100000 + 5;
int A[maxn];
deque<int> que;
int main() {
  int n;
  while (scanf("%d", &n) != EOF) {
    que.clear();
    int d;
    for (int i = 1; i <= n; ++i) {
      scanf("%d", &d);
      que.push_back(d);
    }
    if (n == 1) {
      puts("0");
      continue;
    }
    int ci = n;
    while (*(que.end() - 1) <= *que.begin() && ci > 0) {
      ci--;
      int temp = *(que.end() - 1);
      que.pop_back();
      que.push_front(temp);
    }
    int t = *que.begin(), flag = 0, tt = *que.begin();
    while (!que.empty()) {
      if (t > *que.begin()) {
        flag = -1;
        break;
      }
      t = *que.begin();
      if (t != tt) flag = 1;
      que.pop_front();
    }
    if (flag == -1 || flag == 0)
      printf("%d\n", flag);
    else
      printf("%d\n", n - ci);
  }
  return 0;
}
