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 LittlePonyandSortbyShift {
    public static void main(String args[]){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        Integer arr[] = new Integer[n];
        int index = n;
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
        }
        for (int i = 0; i < n-1; i++) {
            if(arr[i] > arr[i+1]){
                index = i+1;
                break; }
        }
        if(index != n){
            if(arr[index] > arr[0]){
                System.out.println("-1");
                return;
            }
            boolean flag = true;
            for (int i = index; i < n-1; i++) {
                if(arr[i] > arr[i+1]){
                    flag = false;
                    break;
                }
            }
            if(flag){
                for (int i = index; i < n; i++) {
                    if(arr[i] > arr[0]){
                        System.out.println("-1");
                        return;
                    }
                }
            }
            else {
                System.out.println("-1");
                return ;
            }
            System.out.println(n-index);
        }
        else{
                System.out.println("0");
        }
    }
}