A 2-dimensional Turing machine has an infinite "chessboard" as its storage device (one cell for every address (i, j) Element Z times Z). In one step the head moves Left (i--), Right (i ++), Up (j++), or Down (j--). Show that a 2-dimensional TM is not more powerful, i.e., every language accepted by a 2-dimensional TM M is accepted by our standard 1-dim TM M'. To be specific, let's assume the 2-dimensional TM has an additional input tape, form which it only reads (moving in any way), but on which it does not write