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.*;
import java.io.*;

public class LittlePonyandSortbyShift {


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