• 19

## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Goal

A positive integer X is a good number if there exist 5 (not necessarily distinct) positive integers A, B, C, D, and E such that:

1. A + B + C + D = X
2. A + E, B - E, C * E, and D / E are pairwise equal, meaning A + E = B - E = C * E = D / E

The smallest good number is the number 8. This is because there are five positive integers (A, B, C, D, E) = (1, 3, 2, 2, 1) such that:
1. 1 + 3 + 2 + 2 = 8
2. 1 + 1 = 3 - 1 = 2 * 1 = 2 / 1 = 2

You are given N positive integers. For each number, determine whether the number is good or not!
Input
Line 1: An integer N for the number of positive integers given.
Next N lines: An integer X for the positive integer in question.
Output
N lines: A word YES if the number is good, or NO otherwise.
Constraints
1 ≤ N ≤ 100
1 ≤ X ≤ 100000
Example
Input
```4
8
1
69
128
```
Output
```YES
NO
NO
YES
```

A higher resolution is required to access the IDE