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 in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
        int[] c = new int[n];
        boolean b = true;
        int ind = -1, min = 100001;
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
            c[i] = a[i];
            if(i!=0&&c[i]<=min && c[i] != c[i-1]){
                min = c[i];
                ind = i;
            }
        }
        Arrays.sort(c);
        if(Arrays.equals(a, c))
            System.out.println(0);
        else{
            for (int i = 0; i < n; i++) {
                if(c[i] == a[(ind+i)%n])
                    continue;
                else{
                    b = false;
                    break;
                }
            }
            if(b)
                System.out.println(n-ind);
        else
            System.out.println("-1");
        }
    }
}