I think that with this kind of problem, you can process in two steps.
A first easy problem with small N (to test perms for example). And a harder problem with big N, which
oblige to find another algorithm.
http://oeis.org/A000166
3971 Solvers
347 Solvers
123 Solvers
207 Solvers
Generate a random matrix A of (1,-1)
211 Solvers
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