BALKAN-SL 2013 A2

Let $a, b, c$ and $d$ are positive real numbers so that $abcd = \frac14$ . Prove that holds $$\left( 16ac +\frac{a}{c^2b}+\frac{16c}{a^2d}+\frac{4}{ac}\right)\left( bd +\frac{b}{256d^2c}+\frac{d}{b^2a}+\frac{1}{64bd}\right) \ge \frac{81}{4}$$ When does the equality hold?