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.Arrays;
	import java.util.Scanner;
	
	
	public class SortByShift {
	
		public static void main(String[] args) {
			Scanner sc=new Scanner(System.in); 
			int n =sc.nextInt();
			int[]a=new int[n];
			int[]sort=new int[n];
			for (int i = 0; i < a.length; i++) {
				a[i]=sort[i]=sc.nextInt();
				
			}
			
			Arrays.sort(sort);
			int c=0;
			for (int i = 1; i < a.length; i++) {
				if(a[i]<a[i-1])
				{
					c=i;
					break;
				}
			}
			if(c==0)
			{
				System.out.println(0);
			}else {
			
				int ans=0;
				
				for (int i = c, j=0; i < sort.length; i++,j++) {
					
					if(a[i]==sort[j])ans++;
					else{
						ans=-1;
						break;
						
					}
					
				}
				System.out.println(ans);
			}
			
		
		
		
		
		
		}
	}