CN-TST 2014 Problem 9

$A$ is the set of points of a convex $n$ -gon on a plane. The distinct pairwise distances between any $2$ points in $A$ arranged in descending order is $d_1>d_2>...>d_m>0$ . Let the number of unordered pairs of points in $A$ such that their distance is $d_i$ be exactly $\mu _i$ , for $i=1, 2,..., m$ . Prove: For any positive integer $k\leq m$ , $\mu _1+\mu _2+...+\mu _k\leq (3k-1)n$ .