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.*;
import java.nio.charset.MalformedInputException;
import java.util.StringTokenizer;

public class lucky {
static void check1() throws IOException{
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    int x  =Integer.parseInt(bf.readLine());
    int a []=new int [x];
    StringTokenizer st = new StringTokenizer(bf.readLine());
   for(int i = 0;i<x;i++)
       a[i]=Integer.parseInt(st.nextToken());
   int k = 0;
   int count=0;
   boolean flag = false;
   
   for(int i = 1;i<x;i++){
	  if(a[i]<a[i-1]&&flag){
		   System.out.println(-1);
		   return ;
	   }
	   if(a[i]<a[i-1])
	   {
		   k=i;
		   flag = true;
	   }
	   
   }if(a[x-1]>=a[0]&&!flag)
   {
	   System.out.println(0);
	   return ;
   
    
   }
   if(a[x-1]>a[0]&&flag)
   {
	   System.out.println(-1);
	   return ;
   
    
   }
   System.out.println(x-k);
   }
public static void main(String[] args) throws IOException {
	check1();
}
}