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 Little_Pony_and_Sort_by_Shift {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = in.nextInt();
	
		int count=0;
		int index = 0;
		for(int i=1;i<n;i++){
			if(arr[i-1]>arr[i]){
				count++;
				index=i;
			}}
		if(count==0)
			System.out.println("0");
		else if(count>1)
			System.out.println("-1");
		else{
			if(arr[n-1]<=arr[0])
				System.out.println(n-index);
			else
				System.out.println("-1");
		}
}
}