A two-step tree by hand

$S_0=100$, $K=100$, $u=1.1$, $d=0.9$, two periods, gross risk-free return $R=1.05$ per period. (a) Compute the risk-neutral probability. (b) Price the European put and the American put by backward induction. Identify the node where early exercise is optimal. (c) Compute the replicating portfolio $(\Delta,B)$ at the root for the American put and verify that it reproduces the two time-1 values.