For every integer n, let an and bn be real numbers. Let function f : R  $\to$ R be given by
f (x) =  $\{\begin{array}{l}{\mathrm{a}}_{\mathrm{n}}+\mathrm{sin\pi x},\mathrm{for}\mathrm{x}\in [2\mathrm{n},2\mathrm{n}+1]\\ {\mathrm{b}}_{\mathrm{n}}+\mathrm{cos\pi x},\mathrm{for}\mathrm{x}\in (2\mathrm{n}-1,2\mathrm{n})\end{array}$ , for all integers n.

If  f  is continuous, then which of the following hold(s) for all n?