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 Main {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int[] arr = new int[n];
		for(int i = 0;i<n;i++){
			arr[i] = s.nextInt();
		}
		
		boolean seg = false;
		int i = 0;
		int count = 0;
		while(i<n-1){
			if(arr[i]>arr[i+1]){
				seg = true;
				i++;
				break;
			}
			i++;
		}
		if(seg==false){
			System.out.println(0);
			return;
		}
		count = i;
		while(i<n-1){
			if(arr[i]>arr[0]){
				System.out.println(-1);
				return;
			}
			if(arr[i]>arr[i+1]){
				System.out.println(-1);
				return;
			}
			i++;
		}
		if(arr[i]>arr[0]){
			System.out.println(-1);
			return;
		}
		
		System.out.println(n-count);
	}

}