Functions help please

Let $f(x)$ be a monic cubic polynomial, and let  $p(x), q(x)$ and $r(x)$ be polynomials such that $f(x)=p(x)(x-1)+1=q(x)(x-2)+1=r(x)(x-3)+1$
Find $f(4)$

I have tried 1, and f(4) is not 1.

All help is appreciated! Thanks!!!