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 Pins {
    public static void main(String [] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int[] a= new int[n];
        for(int i=0;i<n;i++) {
            a[i] =scan.nextInt();
        }
        int temp=0;
        int x=0;
        for(int i=0;i<n;i++) {
            if(i!=0 && (a[i-1]>a[i])) {
                    temp=i;
                    x++;
            }
        }
        if(x==0) 
        System.out.println("0");
        else if(x==1 && a[n-1]<=a[0])
        System.out.println(n-temp);
        else
        System.out.println("-1");
    }
}