CMO 2000 Problem 2

A permutation of the integers $1901, 1902, \cdots, 2000$ is a sequence $a_1, a_2, \cdots, a_{100}$ in which each of those integers appears exactly once. Given such a permutation, we form the sequence of partial sums $$s_1 = a_1,\; s_2 = a_1 + a_2,\; s_3 = a_1 + a_2 + a_3, \ldots\;, s_{100} = a_1 + a_2 + \cdots + a_{100}.$$ How many of these permutations will have no terms of the sequence $s_1, \ldots, s_{100}$ divisible by three?