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;
import java.util.stream.IntStream;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < a.length; i++) {
			a[i] = sc.nextInt();
		}
		System.out.println(solve(a));

		sc.close();
	}

	static int solve(int[] a) {
		int[] turnIndices = IntStream.range(0, a.length - 1).filter(i -> a[i] > a[i + 1]).toArray();

		if (turnIndices.length == 0) {
			return 0;
		} else if (turnIndices.length == 1 && a[a.length - 1] <= a[0]) {
			return a.length - turnIndices[0] - 1;
		} else {
			return -1;
		}
	}
}
