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 Main {

	public Scanner sc;
	
	public void run() {
		int n = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		int[] sorted = a.clone();
		Arrays.sort(sorted);
		
		int min = sorted[0];
		int minidx = 0;
		int i;
		for (i = n-1; i > 0; i--) {
			if (a[i] == min && a[i-1] != min) {
				minidx = i;
				break;
			}
		}
		
		int idx = minidx;
		for (i = 0; i < n; i++) {
			if (a[idx] != sorted[i]) {
				System.out.println(-1);
				return;
			}
			idx = (idx + 1) % n;
		}
		
		System.out.println(sorted[n-1] == min ? 0 : (n-minidx) % n);
	}
	
    public static void main(String[] args) {
		Main main = new Main();
    	try { main.sc = new Scanner(new FileInputStream("test.in")); }
		catch (FileNotFoundException e) { main.sc = new Scanner(System.in); }
		main.run();
    }

}