Rao-Blackwell builds an unbiased estimate of p squared

You flip a coin with unknown head probability $p$, collecting i.i.d. outcomes $X_1, \dots, X_n$ (each $1$ for heads, $0$ for tails). You want to estimate $p^2$, the probability that two specific flips both come up heads. A crude unbiased estimator is $T = X_1 X_2$, since $\mathbb{E}[X_1 X_2] = p\cdot p = p^2$ by independence.

Rao-Blackwellize $T$ by conditioning on the sufficient statistic $S = \sum_i X_i$, and give the resulting unbiased estimator of $p^2$.