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.Scanner;
public class m2 {
public static void main(String ra[])
{
	Scanner s=new Scanner(System.in);
	int n=s.nextInt();
	int t=0,b=0;
	int a[]=new int[n];
	for(int i=0;i<n;i++)
	{
		a[i]=s.nextInt();
	if(i>0&&a[i-1]>a[i])
	{
		t++;
		b=i;
	}
}
	if(t==0)
		System.out.println("0");
	else if(t==1&&a[n-1]<=a[0])
		System.out.println(n-b);
	else
		System.out.println("-1");
}
}