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) {
        int n;
        Scanner s = new Scanner(System.in);
        n = s.nextInt();
        int[] a = new int[n];
        boolean pico = false;
        for(int i = 0 ; i<n ; i++) {
            a[i] = s.nextInt();
        }
        boolean baje,subi;
        baje=false;
        boolean tr = true;
        int aux = a[0];
        int pos=0;
        int menor = a[0];
        for(int i = 1 ; i < n ; i++) {
            if(a[i]<aux) {
                if(!baje) {
                    if(a[i] <= menor) {
                        baje = true;
                        pos = n-i;
                    }
                    else
                        tr = false;
                }
                else
                    tr = false;
            }
            aux=a[i];
        }
        if(baje) {
            if(a[n-1]>menor)
                tr = false;
        }
        if(tr) {
            System.out.println(pos);
        }
        else
            System.out.println(-1);
    }

}