$(40$P$)$ Any word in a two$-$letter language $(=\{0,8\})$ is written on a transparent strip of paper

$($e$.$g$.08800880).$ When the paper is folded in half, the letters overlap without any errors $($e$.$g$.$

$0880$ : $08800880).$ The paper is folded in half once again. On the transparent paper, the

letters overlap again $($e$.$g$.08$:$8008).$ Let's call this a double palindrome. Design a Turing

machine that accepts these double palindrome words.