For every integer n, let $a_{n}$ and $b_{n}$ be real numbers. Let function $f:R \rightarrow R$ be given by
$f(x)=\begin{cases}a_{n}+\sin \pi x & for x\epsilon[2n,2n+1] \\b_{n}+\cos \pi x & for x \epsilon (2n-1,2n)\end{cases}$
for all integers n,
If f is continuous , then which of the following hold9s) for all n?