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.*;
import java.lang.Math;
public class Main
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
	    int n = sc.nextInt();
	    int a[]= new int[n];
	    for(int i=0;i<n;i++) a[i]=sc.nextInt();
	    int maxi=0;
	    int c=0;
	    int c2=0;
	    for(int i=1;i<n;i++){
	         if(a[i]>=a[i-1]) maxi++;
	         else{
	             c2++;
	             for(int j=i+1;j<n;j++){
	                 if(a[j]<a[j-1]){
	                     c++;
	                     System.out.println(-1);
	                     break;
	                 }
	             }
	         }
	         if(c!=0) break;
	         if(c2!=0){
	             if(a[0]<a[n-1]){
	                 c++;
	                 System.out.println(-1);
	                 break;
	             }
	             break;
	         }
	    }
	    if(c==0) System.out.println(n-1-maxi);
	}
}
