Game tree for a $2$ player sequential game. If P$1$ and P$2$ both pick up$,$ P$1$ gets $$24$ and P$2$ gets $$24.$ If P$1$ picks up and P$2$ picks down, P$1$ gets $$2$ and P$2$ gets $$48.$ If P$1$ picks down and P$2$ picks up$,$ P$1$ gets $$0$ and P$2$ gets $$34.$ If both pick down, P$1$ gets $$18$ and P$2$ gets $$32$

In the game above, what is$/$are the sub$-$game perfect Nash equilibrium?

$($up$,$up$)$

$($up$,$down$)$

$($down$,$ up$)$

$($down$,$ down$)$

No equilibrium exists