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.*;
import java.io.*;
public class Ideone
{
	public static void  main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int ind=-1;
		int a[]=new int[n];
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextInt();
		}
		int c=0;
		for(int i=0;i<n-1;i++)
		{
			if(a[i]>a[i+1])
			{
				ind=i;
				c++;
			}
		}
		if(ind==-1)
		{
			System.out.println(0);
			return;
		}
		if(c>1)
		{
			System.out.println(-1);
			return;
		}
		long min=Integer.MAX_VALUE;
		long max=Integer.MIN_VALUE;
		for(int i=0;i<=ind;i++)
		{
			if(a[i]<min)
				min=a[i];
		}
		
		for(int i=ind+1;i<n;i++)
		{
			if(a[i]>max)
				max=a[i];
		}
		//System.out.println(c);
		if(max<=min)
			System.out.println(n-ind-1);
		else
			System.out.println(-1);
		
	}
} 