In Tetris, Mr. T loves performing Perfect Clears, when a piece clears all lines in the playing field. As you might guess, when it comes to tetriminos, he has a personal favorite: the undeniably cutest O piece. But a Perfect Clear using only O pieces is not terribly exciting, so Mr. T wants to use his second favorite tetrimino: the T piece.
Starting with an empty field, can Mr. T achieve a perfect clear using only T pieces? If so, how fast can he pull it off? Mr. T is not easily persuaded by smooth talk, so please justify your answer with a convincing argument.
The standard Tetris field has ten columns. The T tetrimino has three minos adjacent to a central mino in a T shape, as shown below.