SE-SKOLORNAS 1980 Problem 2

$a_1$ , $a_2$ , $a_3$ , $a_4$ , $a_5$ , $a_6$ , $a_7$ and $b_1$ , $b_2$ , $b_3$ , $b_4$ , $b_5$ , $b_6$ , $b_7$ are two permutations of $1, 2, 3, 4, 5, 6, 7$ . Show that $|a_1 - b_1|$ , $|a_2 - b_2|$ , $|a_3 - b_3|$ , $|a_4 - b_4|$ , $|a_5 - b_5|$ , $|a_6 - b_6|$ , $|a_7 - b_7|$ are not all different.