[problem:https://codeforces.net/contest/1176/problem/B]

So I came across this problem and I would like to implement and idea that after removing values that are directly divisible by 3 and the pairs that add upto sum (divisible by 3), the rem. ones may have some kind of combination of elements with sum adding upto 3

Example:

arr = [1,1,1,1,1,2,2]

after two operations , pairs gets out [1,2],[1,2] with sum(%3==0)

rem = [1,1,1]

Now, how to know that rem array may have some combinations sum divisible by 3?