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 Test {

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int ArraySize , Index = 0 , N = 0;
		ArraySize = input.nextInt();
		int [] Array = new int[ArraySize];
		for(int i = 0 ; i < ArraySize ; i++)
		{
			Array[i] = input.nextInt();
			if(i > 0 && Array[i] < Array[i - 1])
			{
				N++;
				Index = i;
			}
		}
		if(N == 0)
			System.out.println("0");
		else if(N == 1 && Array[ArraySize - 1] <= Array[0])
			System.out.println(ArraySize - Index);
		else
			System.out.println("-1");
	}

}