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 Main {

	public static void main(String[] args) {

		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int a[]=new int[n];
		int k=0;
		int r=0;
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextInt();
			if(i>0&&a[i-1]>a[i])
			{
				k++;
				r=i-1;
			}
		}
		if(k==0)
			System.out.println(0);
		else if(k==1&&a[n-1]<=a[0])
			System.out.println(n-(r+1));
		else
			System.out.println(-1);

	}

}
