Consider the following modification of the classic Tic$-$Tac$-$Toe game which is called Mini Tic$-$Tac$-$Toe. It is played on the

$22$ grid and also has two players, X and O $.$ They take turns $($starting from X $)$ placing their marks in any empty cell of the

grid until either one player wins or there are no available cells left $($note that if a player wins, the game immediately ends$).$

A player wins if she is the first to align two marks in a horizontal or vertical line $($note that diagonal lines do not count for

winning$).$ Call the cells A$,$ B$,$ C$,$ and D $($in the clockwise order strating from northwest$)$ for ease of notation.

$($a$)$ Represent the game in extensive form. Make sure the tree is correctly labeled ${?}^1$ and all legal moves are included.

$($b$)$ H

$($c$)$ Hov

$($d$)$ Rep

${?}^1$ It is up to you how to customize the labels for the branches, but perhaps using lowercase and uppercase letters along with numerical subscripts when necessary

would be the most straigtforward.