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.*;

public class B454 {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		
		int[] ar = new int[n];
 		for (int i = 0; i < n; i++) {
			ar[i] = scan.nextInt();
		}
 		
 		int ind = 0;
 		int cnt = 0;
 		int min = Integer.MAX_VALUE;
 		
 		for (int i = 1; i <= n; i++) {
 			if (ar[i % n] < ar[i - 1]) {
 				cnt++;
 				if (cnt > 1) {
 					System.out.print("-1");
 	 				System.exit(0);
 				}
 				ind = i % n;
 			}
 		}
 		
 		System.out.print(ind == 0 ? 0 : n - ind);
	}
}