Change of Variables & the Jacobian · Medium problem

Let $R$ be the parallelogram with vertices $(0,0)$, $(2,1)$, $(1,2)$, $(3,3)$. Using the substitution $x=2u+v$, $y=u+2v$ (which sends the unit square $0\le u,v\le1$ onto $R$), evaluate $\displaystyle\iint_R xy\,dA$.