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
//  30/07/20  7:56 PM  Jul  2020 

import java.io.*;
import java.util.*;

public class _454B {

    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 idx = 0, inc = 0;
        //if all increasing then print 0;
        for (int i = 0; i < n - 1; ++i) {
            if (arr[i + 1] >=arr[i]) {
                inc++;
            }
        }
        if (inc == n - 1)
            System.out.println("0");
        else {
            //if we have more then one breakpoint then print -1
            int dec=0;
            for (int i = 0; i < n - 1; ++i) {
                    if(arr[i]>arr[i+1]) {
                        dec++;
                        idx = i;
                    }
            }
            if(dec>1)
                System.out.println("-1");
            else {
                boolean check = true;
                for (int i = idx + 1; i < n; i++) {
                    if (arr[i] > arr[0]) {
                        check = false;
                        break;
                    }
                }
                if (check)
                    System.out.println(n - (idx + 1));
                else
                    System.out.println("-1");
            }
        }
    }
}