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.Arrays;
import java.util.Scanner;


public class LittlePony {
    
    public static boolean Sorted(int [] a) { 
        for (int i = 1; i < a.length; i++) {
            if(a[i]<a[i-1]) return false;
        }
        return true;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int [] a = new int[n];
        a[0] = sc.nextInt();
        int pos = 0;
        int nums = 0;
        boolean found = false;
        for (int i = 1; i < a.length; i++) {
            a[i] = sc.nextInt();
            if(a[i]<a[i-1] && !found){
                nums = a.length - i;
                pos = i;
                found = true;
            }
        }
        int [] b = new int[n];
        int j = 0;
        boolean ok = true;
        for (int i = 0; i < a.length; i++) {
            if(pos < a.length)
            b[i] = a[pos++];
            else
                b[i] = a[j++];
        }
        if(Sorted(b))
            System.out.println(nums);
        else
            System.out.println(-1);

        }
        
    }
