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 _454B_Little_Pony_and_Sort_by_Shift {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] a = new int[n];
		int[] c = new int[n];
		int start = 0;

		for (int i = 0; i < n; i++)
			a[i] = in.nextInt();

		for (int i = 1; i < n; i++)
			if (a[i] < a[i - 1]) {
				start = i;
				break;
			}

		for (int i = 0; i < c.length; i++)
			c[i] = a[(i + start) % n];

		if (isSorted(c))
			System.out.println((n - start)%n);
		else
			System.out.println(-1);
	}

	private static boolean isSorted(int[] a) {
		for (int i = 1; i < a.length; i++)
			if (a[i - 1] > a[i])
				return false;
		return true;
	}
}
