Let $\displaystyle R = [a,b]\times[c,d]$ be a rectangle $\displaystyle ( d(ab) = d(cd); d(ac) = d(bd) )$ and let $\displaystyle R_i = (a_i,b_i)\times(c_i,d_i)$, ($\displaystyle 1\leq i \leq n$) be rectangles inside R, such that every two rectangles in R are disjoint, maybe other than their sides, and such that each one of them has at least one integer side.

Also,

$\displaystyle \bigcup_{1\leq i \leq n}R_i = R$

Prove that R also has at least one integer side.