CF1515B Phoenix and Puzzle

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 pieceThe 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?

N/A

N/A

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.