A permutation of the integers \(2020, 2021,...,2118, 2119\) is a list \(a_1,a_2,a_3,...,a_{100}\) where each one of the numbers appears exactly once. For each permutation we define the partial sums. $s_1=a_1$ $s_2=a_1+a_2$ $s_3=a_1+a_2+a_3$ $...$ $s_{100}=a_1+a_2+...+a_{100}$ How many of these permutations satisfy that none of the numbers \(s_1,...,s_{100}\) is divisible by $3$?