Draw the checkerboard after dividing it into $4$ sub$-$checkerboards such that:

each sub$-$checkerboard is a square, and

each sub$-$checkerboard contains exactly either a missing cell $("0")$ or a cell

covered by a triomino.

Hint: Place a triomino at a suitable location to divide the checkerboard.

$3($b$)$ We represent the checkerboard by using a two$-$dimensional integer array

$A[0..m-1,0..m-1],$ where $m$ is a power of two. For example, the value of $m$ can be $2,4,$

$8,16,32,$dots.. Suppose that, in the two$-$dimensional array $A,$ the missing cell is set to

$0$ and the other cells are initialized to $-1.$

Write an algorithm $($i$.$e$.,$ pseudo$-$code$)$ using divide$-$and$-$conquer to fill the two$-$

dimensional array $A[0..m-1,0..m-1]$ to satisfy all the following conditions:

all cells $($except the missing cell$)$ are assigned positive integers,

only the cells belonging to the same triomino can be assigned the same integer.

Please refer to the sample output in Figure $1($b$).$