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 _454B_SortByShift {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int[] A = new int[n];
		int count = 0;
		int first = -1;
		A[0] = s.nextInt();
		for (int i = 1; i < n; i++) {
			A[i] = s.nextInt();
			if (A[i-1] > A[i]) {
				count++;
				first = i-1;
			}
		}
		if (count == 0) {
			System.out.print(0);
		} else if (count == 1 && A[0] >= A[n-1])
			System.out.print(n-1-first);
		else
			System.out.print(-1);
	}

}
