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.io.*;
import java.util.*;

public class cp
{
	public static void main(String[] args) throws IOException
	{
		try{
			//Your Solve
			Scanner s = new Scanner(System.in);
			int n = s.nextInt();
			int[] arr = new int[n];
			arr[0] = s.nextInt();
			int count = 0;
			int index = 0;
			for(int i = 1;i < n;i++) {
				arr[i] = s.nextInt();
				if(arr[i] < arr[i-1]){
					count += 1;
					index = i;
				}
			}
			if(count == 1){
				if(arr[n-1] <= arr[0]) {
				System.out.println(n-index);
				}else {
					System.out.println(-1);
				}
			}else if(count == 0){
				System.out.println(0);
			}else{
				System.out.println(-1);
			}
			
			
			
		}catch(Exception e){
			return;
		}
	}
}