An analyst considers a $2$ period binomial lattice model. The first $3$ nodes of the European call option's nodes were as follows $25\mathrm{.}5,5\mathrm{.}3,28\mathrm{.}3$ Determine the options payoffs at nodes N$4,$ N$5,$ N$6$ given that for the call at node N$7$ is $54$ payoff given risk$-$free rate is zero

$(6$ marks$)$