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 G {
 
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
        int start = 0;
        
        int needsort = 0;
        int cansort = 1;
        for (int i = 0; i < n; i++) {
            a[i]= in.nextInt();
            if(i > 0 && a[i] < a[i-1]){
                needsort = 1;
                start = i;
                i++;
                
                while(i < n ){
                    a[i]= in.nextInt();
                    if(  a[i] < a[i-1] ){
                        cansort = 0;
                        break;
                    }
                    i++;
                    
                }
            }
        }
        
        if(needsort == 0){
            System.out.println(0);
        }
        else if(needsort == 1 && cansort == 0)System.out.println(-1);
        else if(needsort == 1 && cansort == 1 && a[n-1]<= a[0]){
            
                System.out.println( n - start );
            
        }
        else
            System.out.println(-1);
        
    }
}
