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;

/**
 * Created by amatskoff on 01.08.14.
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        StringBuilder output = new StringBuilder();

        int n = scanner.nextInt();
        int jumpIndex = -1;
        int prevValue = scanner.nextInt();
        int firstValue = prevValue;

        for(int i = 1; i < n; i++) {
            int currValue = scanner.nextInt();
            if(currValue < prevValue && jumpIndex == -1) {
                jumpIndex = i;
            } else if(currValue < prevValue && jumpIndex != -1) {
                System.out.println("-1");
                return;
            }

            prevValue = currValue;
        }

        if(jumpIndex != -1 && prevValue > firstValue) {
            System.out.println("-1");
            return;
        }

        if(jumpIndex == -1) {
            System.out.println("0");
            return;
        }

        System.out.println(n - jumpIndex);

    }
}
