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.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

/**
 * Created by ctash on 21.03.2015.
 */
public class Pony2 {

    public static void main(String[] args) {
        Scanner sc = new Scanner(new InputStreamReader(System.in));

        int size = sc.nextInt();
        List<Integer> arrayList = new ArrayList<Integer>();

        for (int i = 0; i < size; i++) {
            final int nextInt = sc.nextInt();
            arrayList.add(nextInt);
        }
        sc.close();
        int prevInt = arrayList.get(0);
        int border = -1;
        for (int i = 1; i < size; i++) {
            final Integer nextInt = arrayList.get(i);
            if (nextInt >= prevInt) {
                prevInt = nextInt;
            } else {
                if (border != -1) {
                    System.out.println(-1);
                    return;
                }
                border = i;
                prevInt = nextInt;
            }
        }
        if (border != -1 && arrayList.get(size - 1) > arrayList.get(0)) {
            System.out.println(-1);
            return;
        }
        if (border == -1) {
            System.out.println(0);
            return;
        }
        System.out.println(size - border);
        return;

    }

}
