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You might need to take a principled approach to this one.
Clive, thanks a lot! The problem immeadieately feels as related to some other well-known - but this doesn't help :)
I would like to know the meaning of "principled" in this case - such a situation when, seeminly, the word is familiar but sense is hard to catch :)
Problem is live for some time already, and I see Vladimir and Mathias already proof-solved it, great work!
Rodion, thanks for posting the solution; and Mathias and Vladimir thanks for showing that everything is working.
Rodion, my statement above was intended as a clue to the solution. Does removing the "d" to leave "principle" make any more sense?