Question 19
Determine the largest possible value of
$$
S = a_1 a_2 a_3 + a_4 a_5 a_6 + \dots + a_{2017} a_{2018} a_{2019} + a_{2020},
$$
where $(a_1, a_2, a_3, \dots, a_{2020})$ is a permutation of $(1, 2, 3, \dots, 2020)$.
$$
S = a_1 a_2 a_3 + a_4 a_5 a_6 + \dots + a_{2017} a_{2018} a_{2019} + a_{2020},
$$
where $(a_1, a_2, a_3, \dots, a_{2020})$ is a permutation of $(1, 2, 3, \dots, 2020)$.