Description

Given a list of n different numbers, which number in this list can be represented as an average of any two other numbers in the same list?

Input

There are multiple test cases.

The first line of each test case is an integer n, where 3 ≤ n ≤ 1000. The second line contains n different positive integers seperated by spaces, denoting the list of numbers. The numbers are in ascending order and every number in this list is less than 10⁹.

Output

For each test case, output the number of numbers in this list which can be represented as an average of any two other numbers in the same list.

Sample

3
1 2 3
6
3 4 6 7 8 9

1
3

Hint

In the first case, 2 can be represented by (1 + 3) / 2.

In the second case, 6 can be represented by (3 + 9) / 2, 7 can be represented by (6 + 8) / 2, 8 can be represented by (7 + 9) / 2.