CWMO 2015 Problem 1

Let the integer $n \ge 2$ , and $x_1,x_2,\cdots,x_n$ be real numbers such that $\sum_{k=1}^nx_k$ be integer . $d_k=\underset{m\in {Z}}{\min}\left|x_k-m\right|$ , $1\leq k\leq n$ .Find the maximum value of $\sum_{k=1}^nd_k$ .