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;
import java.util.Collections;
import java.util.ArrayList;
import java.util.Arrays;
import java.io.PrintWriter;

public class p454B{
	public static void main(String []args)
	{
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
			int n  = in.nextInt();
			int t = 0, b = 0;
			int arr[] = new int[n];
			for(int i=0; i< n; i++)
			{
				arr[i] = in.nextInt();
				if(i>0 && arr[i]<arr[i-1]){
					t++;
					b = i;
				}
			}
			if(t==0) out.println("0");
			else if(t==1 && arr[n-1]<=arr[0]) out.println((n-b));
			else out.println("-1");
		out.flush();
	}
}