CMO 1998 Problem 2

Given a positive integer $n>1$ , determine with proof if there exist $2n$ pairwise different positive integers $a_1,\ldots ,a_n,b_1,\ldots b_n$ such that $a_1+\ldots +a_n=b_1+\ldots +b_n$ and $$n-1>\sum_{i=1}^{n}\frac{a_i-b_i}{a_i+b_i}>n-1-\frac{1}{1998}.$$