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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class TaskB259 {
    /**
     * @param args
     */
    public static void main(String[] args) {
        TaskB259 task = new TaskB259();
        task.read();
        task.write();
    }

    int n;
    int a[];

    public void read() {
        InputStreamReader bin = new InputStreamReader(System.in);
        BufferedReader brin = new BufferedReader(bin);
        Scanner in = new Scanner(brin);
        n = in.nextInt();
        a= new int[n];
        for (int i = 0; i <  n; i++) {
            a[i] = in.nextInt();
        }
        in.close();
    }


    public void write() {
        PrintWriter out = new PrintWriter(System.out);
        List<Triple> list = new ArrayList<>();
        int prev = 0;
        for (int i = 1; i <= n; i++) {
            if (i == n || a[i] < a[i - 1]) {
                list.add(new Triple(prev, i - 1));
                prev = i;
            }
        }
        int res = 0;
        int m = list.size();
        for (int i = 1; i < list.size(); i++) {
            if (a[list.get((1 + i) % m).start] >= a[list.get(i).end]) {
                res += list.get(i).end - list.get(i).start + 1;
            } else {
                res = -1;
                break;
            }
        }
        out.print(res);
        out.close();
    }

    private static class Triple {
        int start;
        int end;

        private Triple(int start, int end) {
            this.start = start;
            this.end = end;
        }
    }

}