Let $a, b, c, d$ be positive real numbers. It is given that at least one of the following two conditions holds: $$ab >\min(\frac{c}{d}, \frac{d}{c}), cd >\min(\frac{a}{b}, \frac{b}{a}).$$Show that at least one of the following two conditions holds: $$bd>\min(\frac{c}{a}, \frac{a}{c}), ca >\min(\frac{d}{b}, \frac{b}{d}).$$