Junior Balkan Mathematical Olympiad 2021 - Problem 2 - 1 July 2021

Problem 2. For any set $A = \{x_1, x_2, x_3, x_4, x_5\}$ of five distinct positive integers denote by $S_A$ the sum of its elements, and denote by $T_A$ the number of triples $(i, j, k)$ with $1 \le i < j < k \le 5$ for which $x_i + x_j + x_k$ divides $S_A$ .
Find the largest possible value of $T_A$ .