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.*;

public class B454{
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int a[] = new int[n];
		int dec = 0;
		int decIndex=-1;
		int maxi = 0;
		int mini = Integer.MAX_VALUE;
		a[0] = in.nextInt();
		mini = a[0];
		for(int i=1;i<n && dec<2;i++){
			a[i] = in.nextInt();
			if(a[i]>=a[i-1]){
				if(dec==0){
					mini=Math.min(mini, a[i]);
				}
				else{
					maxi=Math.max(maxi, a[i]);
				}
			}
			else{
				dec++;
				decIndex=i;
				maxi = a[i];
			}

		}
		// System.out.println(dec+" "+decIndex);
		// System.out.println(maxi+" "+mini);
		if(dec==0){
			System.out.println(0);
		}
		else if(dec==1 && mini>=maxi){
			System.out.println(n-decIndex);
		}
		else{
			System.out.println(-1);
		}
	}
}