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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        int[] c = new int[n];
        StringTokenizer st = new StringTokenizer(in.readLine());
        for(int i = 0; i < n; i++)
            c[i] = Integer.parseInt(st.nextToken());
        int a = 0;
        int b = 0;
        for(int i = 1; i < n; i++)
            if(c[i] < c[i - 1]) {
                a++;
                b = i;
            }
        if(a == 0)
            System.out.println(0);
        else if(a > 1) {
            System.out.println(-1);
        } else {
            if(c[n - 1] <= c[0])
                System.out.println(n - b);
            else
                System.out.println(-1);
        }
    }
}
