VMO 2020 Problem 2

a)Let $a,b,c\in\mathbb{R}$ and $a^2+b^2+c^2=1$ .Prove that: $|a-b|+|b-c|+|c-a|\le2\sqrt{2}$ b) Let $a_1,a_2,..a_{2019}\in\mathbb{R}$ and $\sum_{i=1}^{2019}a_i^2=1$ .Find the maximum of: $S=|a_1-a_2|+|a_2-a_3|+...+|a_{2019}-a_1|$