USAMO 1998 Problem 1

Suppose that the set $\{1,2,\cdots, 1998\}$ has been partitioned into disjoint pairs $\{a_i,b_i\}$ ( $1\leq i\leq 999$ ) so that for all $i$ , $|a_i-b_i|$ equals $1$ or $6$ . Prove that the sum $$|a_1-b_1|+|a_2-b_2|+\cdots +|a_{999}-b_{999}|$$ ends in the digit $9$ .