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.*;
import java.util.Arrays;
import java.util.Scanner;
public class Main {
    public static void main(String[] args) throws IOException {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] arr = new int[n];
        int[] newArr = new int[n];
        boolean check = false;
        arr[0] = in.nextInt();
        int index = -1;
        for (int i = 1; i < arr.length; i++) {
            arr[i] = in.nextInt();
            if (arr[i] < arr[i-1] && !check){
                index = i;
                check = true;
            }
        }

        if (check){
            System.arraycopy(arr, index, newArr, 0, arr.length-index);
            System.arraycopy(arr, 0, newArr, arr.length-index, index);
            Arrays.sort(arr);
            System.out.println(Arrays.equals(arr, newArr) ? arr.length-index : -1);
        }else System.out.println(0);

    }
}
