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
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] num = new int[N];
        for (int i = 0; i < N; i++)
            num[i] = sc.nextInt();
        sc.close();

        int cnt = 0;
        int index = 0;
        for(int i = 1; i < N; i++) {
            if(num[i-1] > num[i]) {
                ++cnt;
                index = i;
            }
        }

        if(cnt == 0) {
            System.out.println(0);
        } else if(cnt > 1) {
            System.out.println(-1);
        } else {
            if(num[N-1]  <= num[0]) {
                System.out.println(N - index);
            } else {
                System.out.println(-1);
            }
        }
    }
}
