Real numbers y, p, and n (all greater than 1) satisfy \((\log_{p^{1/n}}…

Real numbers y, p, and n (all greater than 1) satisfy $(\log_{p^{1/n}} y)(\log_{y^{1/n}} p) = 16$, where the logarithms are taken to the bases $p^{1/n}$ and $y^{1/n}$. The value of n is ________