> For every string, you can keep track of this sum incrementally.
> When the string establishes a new adjacency to an empty point i,
> you add code[i] into the sum.
OK that's what I thought before then I got really confused. And nums
is just U_all_i code[i], right?
> > if sum a_i <= 4, and sum (a_i * n_i) is in {1,2,3,4} * nums,
> > then only one a_i is nonzero.
So a_i could be 2 and sum(a_i * n_i) could be in 4*nums (for example)
and this would mean that we are in atari? We are not only interested
in whether sum(a_i * n_i) is in sum(a_i) * nums?
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