An analyst considers pricing a European put option using a $2$ period binomial lattice approach. The option payoffs at the nodes in his model for Period $1$ and Period $2$ are estimated to be:

$\backslash$table$[[,0],[5\mathrm{.}29,],[,18],[28\mathrm{.}23,18],[,54]]$

Determine the analyst's Price of the European put option at $t=0.$

$(6$ marks$)$