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.Scanner;

public class B {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int ans = 0;
		int max = 0;
		int[] ar = new int[n];
		for (int i = 0; i < n; i++) {
			ar[i] = in.nextInt();
			if (i > 0) {
				if (ar[i] < ar[i - 1]) {
					if (ans == 0) {// age dafe aval in etefagh oftade moshkeli
									// nadare
						ans++;
						max = ar[i];
					} else {
						ans = -1;
						break;
					}
				}

				else {// age anasore bad az oon adad soudi beshan
					if (ans != 0) {
						ans++;
						max = ar[i];
					}
				}
			}
		}
		if (max > ar[0])
			ans = -1;
		System.out.println(ans);
	}
}
