ELMO 2013 Problem 1

Let $a_1,a_2,...,a_9$ be nine real numbers, not necessarily distinct, with average $m$ . Let $A$ denote the number of triples $1 \le i < j < k \le 9$ for which $a_i + a_j + a_k \ge 3m$ . What is the minimum possible value of $A$ ?

Proposed by Ray Li