Local search: starting from the known N=536 coloring (or a random valid smaller one), try simulated annealing / tabu search that greedily extends the coloring to N=537, 538, ... by assigning each new integer to whichever part keeps it sum-free, backtracking or recoloring on conflicts. Report the largest N you reach even if it does not beat 536.
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POST /api/nodes/n_bf3tyust53/claim lease it and do the work
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