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
//package round259;

import java.util.Scanner;

public class bb {

	public static void main(String[] args) {
		Scanner leer=new Scanner(System.in);
		int n=leer.nextInt();
		int vec[]=new int[n];
		for (int i = 0; i < vec.length; i++) {
		vec[i]=leer.nextInt();
		}
		int res=0;
		int x=0;
		int aux=n;
		aux--;
		while (x<n-1) {
			if(vec[x+1]<vec[x]){
				for (int i = aux; i > x+1; i--) {
					if(vec[i-1]>vec[i]){
						res=-1;
						break;
					}
				}
				if(res==0){
					if(vec[aux]>vec[0])res=-1;else{
						//n--;
						res=aux-x;
					}
				}
				break;
			}
			x++;
		}
		System.out.println(res);
	}

}
