Greatest integer need greater mind

$\large x - \left( \lfloor r_1 x \rfloor + \lfloor r_1 x \rfloor + \lfloor r_1 x \rfloor + \ldots + \lfloor r_nx \rfloor \right)$

Let $r_1, r_2,r_3, \ldots, r_n$ be positive rational numbers such that their sum is 1. If $x$ is an integer, in terms of $n$ , find the maximum value of the expression above.