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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main{
    public static void main (String[] args){
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = in.nextInt();
        int[] a = new int[n];
        for (int c = 0; c<n; c++){
            a[c] = in.nextInt();
        }
        
        int min = n;
        boolean bajo = false, todobien = true;
        for (int c = 1; c<n && todobien; c++){
            if (a[c-1] > a[c]){ 
                if (bajo) {
                    todobien = false;
                } else {
                    bajo = true;
                    min = c;
                    if (a[a.length-1]>a[0]){
                        todobien = false;
                    }
                }
            }
        }
        if (todobien){
            System.out.println(a.length - min);
        } else {
            System.out.println("-1");
        }
}
}