CMO 1991 Problem 4

Can ten distinct numbers $a_1, a_2, b_1, b_2, b_3, c_1, c_2, d_1, d_2, d_3$ be chosen from $\{0, 1, 2, \ldots, 14\}$ , so that the $14$ differences $|a_1 - b_1|$ , $|a_1 - b_2|$ , $|a_1 - b_3|$ , $|a_2 - b_1|$ , $|a_2 - b_2|$ , $|a_2 - b_3|$ , $|c_1 - d_1|$ , $|c_1 - d_2|$ , $|c_1 - d_3|$ , $|c_2 - d_1|$ , $|c_2 - d_2|$ , $|c_2 - d_3|$ , $|a_1 - c_1|$ , and $|a_2 - c_2|$ are all distinct?