A $4$ by $4$ tic$-$tac$-$toe board is an $2-$dimensional array of char in which each element is either an $\text{'}$X$\text{'},\text{'}$O$\text{'}$ or $\text{'}-$

$\text{'}.$ The game is like normal tic$-$tac$-$toe but the players may keep playing even after someone has three in a row. After the board is full, the winner is whichever player with the most "threes in a row".

a$)$ Calculate $n=$ the number of possible boards, without regard for the rules of tic$-$tac$-$toe. For example we'll include boards with $5$ X$\text{'}$s and $2$ O$\text{'}$s even though no such board could occur in an actual game.

b$)$ In $C++,$ write a perfect minimal hash function hash$1$ that maps each board to a unique value between $0$ and $n-1($provided tableSize $n),$ where $n$ is your value from Part a$.$

unsigned int hash$1($char board$[4][],$ unsigned int tableSize$)$;