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.Scanner;

public class last_first_sorting {
public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int [] sort = new int[N];
        for(int i=0;i<N;i++) {
            sort[i]=in.nextInt();
        }
        int ans=N-1;
        for(int i=0;i<N;i++) {
            if(sort[i]>sort[(i+1)%N]) {
                if(ans!=N-1) {
                    System.out.println("-1");
                    return;
                }
                ans=i;
            }
        }
        System.out.println(N-1-ans);
    }
}
