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.*;

public class LittlePonyAndSortByShift
{
    public static void main(String[] args)
    {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int[] numbers = new int[n];
        for (int x = 0; x < n; x++)
        {
            numbers[x] = input.nextInt();
        }
        int count = 0;
        boolean possible = true;
        int index = 0;
        for (int x = 1; x < n; x++)
        {
            if (numbers[x] < numbers[x - 1])
            {
                count++;
                index = x;
                if (numbers[numbers.length - 1] > numbers[0])
                {
                    System.out.println(-1);
                    possible = false;
                    break;
                }
            }
            if (count == 2)
            {
                System.out.println(-1);
                possible = false;
                break;
            }
        }
        if (possible)
        {
            if (count == 0)
            {
                System.out.println(0);
            }
            else
            {
               System.out.println(n - index); 
            }
        }
    }
}