Consider a static sequential move game where player $1$ moves first, then player $2.$ Player $1$ gets to choose to move Up or Down. Player $2$ gets to move Left or Right. If player $1$ moves Up and player $2$ moves Left, payoffs are $(10,4)($where $10$ is the playoff for player $1$ and $4$ is the payoff for player $2).$ If player $1$ moves Up and player $2$ moves Right, payoffs are $(100,2).$ If player $1$ moves Down and player $2$ moves Left, payoffs are $(4,15).$ If player $1$ moves Down and player $2$ moves Right, payoffs are $(7,12).$

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A$)$ Formalize the game tree to this game.

B$)$ Determine the Subgame Perfect Nash Equilibrium $($SPNE$).$

C$)$ Suppose now that player $2$ gets to move first. What is the SPNE? Does it differ from part B$)?$ Why or why not?