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This problem requires some elementary geometry
It's ready, thanks Clive!
If anyone experience difficulty with the length of input string (it is not particularly large, but probably some editors and clipboard software may misbehave) - please tell, I think we can split lines if necessary!
UPD: very pleasing problem, thanks once more - not difficult but requires some thinking / inventiveness... and matches my skills :)
I'm glad you liked the problem. Many thanks for the helpful graphic which you have added.