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.*;

public class B {

    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        int n = Integer.parseInt(br.readLine()), idx = 0;
        StringTokenizer s = new StringTokenizer(br.readLine());
        int[] arr = new int[n];
        arr[0] = Integer.parseInt(s.nextToken());
        int min = arr[0];
        for (int i = 1; i < arr.length; i++) {
            arr[i] = Integer.parseInt(s.nextToken());
            if (arr[i] < min) {
                min = arr[i];
                idx = i;
            } else if (arr[i] == min && arr[i] != arr[i - 1]) {
                min = arr[i];
                idx = i;
            }
        }
       
        for (int i = idx, j = 1; j < n; i++, j++) {
            int r = arr[i % n];
            int l = arr[(i + 1) % n];
           
            if (l < r) {

                System.out.println("-1");
                System.exit(0);
            }
        }
        System.out.println(idx == 0 ? "0" : (n - idx));
        out.flush();
        out.close();
    }

}
