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 matt on 1/20/17.
 */
public class CF454B_D {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] nums = new int[n];
        int min = 100000;
        int index = -1;
        for (int i = 0; i < n; ++i) {
            int tmp = sc.nextInt();

            if (min > tmp) {
                min = tmp;
                index = i;
            }

            nums[i] = tmp;
        }

        int count = 0;
        for (int i = 1; i < n; ++i) {
            if (nums[i - 1] > nums[i]) {
                count++;
                index = i;
            }

        }
        if (count == 0) {
            System.out.println(0);
        } else if (count > 1) {
            System.out.println(-1);
        } else {
            if (nums[n - 1] <= nums[0]) {
                System.out.println(n - index);
            } else System.out.println(-1);
        }
    }


}
