Comparing Two Inscribed Squares in a Right Triangle

As shown in the figure, $\triangle ABC$ has a right angle at $C$, and two squares are inscribed in it. Square $CPQR$ has its vertex at $C$, with $P$ on $CB$, $Q$ on $AB$, and $R$ on $CA$; square $MSTN$ has its side $ST$ on the hypotenuse $AB$, with $M$ on $CB$ and $N$ on $CA$. Let their areas be $S_1$ and $S_2$ respectively. Determine, with proof, which of $S_1$ and $S_2$ is larger.