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.io.IOException;
import java.util.*;
public class littlePonyAndSortNyShift 
{
 public static void main(String[] args)
	{
 	      Scanner input = new Scanner(System.in);
              int n = input.nextInt();
              int count = 0;
              int temp = 0;
              int arr[]= new int[n];
               for(int i =0;i<n;i++)
		{
                   arr[i]= input.nextInt();
                   if(i>0 && arr[i]<arr[i-1])
		   {
                       count++;
                       temp = i;
                   }
               }
               
               if(count==0)
	       {
                   System.out.println(0);
               }
		else if(count==1 && arr[n-1]<=arr[0])
		{
                   System.out.println(n-temp);
               }
		else
		{
                   System.out.println(-1);
                }
             
             } 
        } 
