NxNxN Solver

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Permutation Networks
24 12 12 4 4 4 4 4 4
Each center orbit reduces 24 → 12 · 12, then every 12 splits 12 → 4 · 4 · 4 (twice) — a C-shaped permutation network.
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N must be even
brob2 generates a uniformly-random center configuration internally