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.io.*;
import java.util.*;
import java.lang.*;

public class Rextester{
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = new Integer(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        br.close();
        int[] array = new int[n];
        for(int i=0;i<n;i++){
            array[i]=new Integer(st.nextToken());
        }
            int i,j;
            for(i=n-1;i>0;i--){
                if(array[i]<array[i-1]){
                    break;
                }
            }
            for(j=0;j<n-1;j++){
                if(array[j]>array[j+1]){
                    break;
                }
            }
            if(i==0&&j==n-1){
                System.out.println("0");
            }
            else if(j+1==i&&array[0]>=array[n-1]){
                System.out.println(n-i);
            }
            else{
                System.out.println("-1");
            }
    }
}
            
        