Let $p > 1$ and let $a, b, c, d$ be positive numbers such that $$(a + b + c + d) \left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}\right)= 16p^2.$$Find all values of the ratio $ R =\frac{\max \{a, b, c, d\}}{\min \{a, b, c, d\}}$ (depending on the parameter $p$)