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 sidharth on 19/9/15.
 */
public class LittlePonyAndSort {
    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int[] arr = new int[n];

        for (int i = 0; i < n; i++) {

            arr[i] = sc.nextInt();
        }

        int min = arr[0];
        int index = 0;




        for (int i = 1; i < n; i++) {

            if (arr[i - 1] > arr[i] ) {

                index = i;

                if(arr[index] > min){

                    System.out.print(-1);
                    return;
                }


                for(int j = index ; j < n - 1; j++){

                    if(arr[j ] > arr[j + 1] || arr[j + 1] > min){

                        System.out.print("-1");
                        return;
                    }
                }
                System.out.print(n - index);
                return;

            }
        }

        System.out.print(0);


    }
}
