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 Test {
    public static void main(String[] args){
        Scanner cin = new Scanner(System.in);
        int n = cin.nextInt();
        int a[] = new int[n];
        for(int i = 0; i < n;i++){
            a[i] = cin.nextInt();
        }
        int flag = 0;
        int pos = -1;
        for(int i = 1; i < n; i++){
            if(a[i-1] > a[i]){
                flag++;
                if(flag == 1){
                    pos = i;
                }
            }
        }
        if(flag == 0){
            System.out.println("0");
        }
        else if(flag > 1){
            System.out.println("-1");
        }
        else {
            if(a[n-1] > a[0]){
                System.out.println("-1");
            }
            else{
                System.out.println(n-pos);
            }
        }
    }
        
}