1515B · Phoenix and Puzzle

Problem: Phoenix is playing with a new puzzle, which consists of $n$ identical puzzle pieces. Each puzzle piece is a right isosceles triangle as shown below.

A puzzle piece

The goal of the puzzle is to create a square using the $n$ pieces. He is allowed to rotate and move the pieces around, but none of them can overlap and all $n$ pieces must be used (of course, the square shouldn't contain any holes as well). Can he do it?

Input Format: The input consists of multiple test cases. The first line contains an integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains an integer $n$ ($1 \le n \le 10^9$) — the number of puzzle pieces.

Output Format: For each test case, if Phoenix can create a square with the $n$ puzzle pieces, print YES. Otherwise, print NO.

Note: For $n=2$, Phoenix can create a square like this:

For $n=4$, Phoenix can create a square like this:

For $n=6$, it is impossible for Phoenix to create a square.