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 B
{
    public static int solve(int[] arr)
    {
    try{
        int idxMin =0;
        for(idxMin = 0; idxMin < arr.length-1; idxMin++)
        {
            if(arr[idxMin] > arr[idxMin+1])
            {
                idxMin++;
                break;
            }
            else if(idxMin+1 == arr.length-1)
            {
                return 0;//already sorted
            }
        }
        for(int i = idxMin; i < arr.length-1; i++)
        {
            if(arr[i] > arr[i+1]){
                return -1;
            }
        }
        int temp = arr[arr.length-1];
        if(temp > arr[0])
            return -1;
        for(int i = 0; i < idxMin-1; i++)
        {
            if(arr[i] > arr[i+1]){
                return -1;
            }
        }
        return arr.length-idxMin;
    }
    catch(Exception e)
    {
        return -1;
    }
    
    }

    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = Integer.parseInt(in.next());
        int[] arr = new int[n];
        for(int i = 0; i < n; i++)
            arr[i] = Integer.parseInt(in.next());
        n = solve(arr);
        System.out.println(n);
        
    }
}