Let $f:(0,\infty ) \to {\bf{R}}$ be a twice differentiable function. If for some ${\rm{a}} \ne 0,\int_0^1 f (\lambda x){\rm{d}}\lambda = {\rm{a}}f(x),f(1) = 1$ and $f(16) = \frac{1}{8}$, then $16 - f'\left( {\frac{1}{{16}}} \right)$ is equal to _________ .
