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05AB1E, 80 77 73 72 77 74 bytes ₂Ý8+3ä€ü3€`4иML3δи©«4㮀¦©âʒ˜D¢à5‹}®7.Æ«8L•1«þï•₆в«D¸â«ε˜•1óñ•+çJœIœδ.L}W< -5 bytes thanks to @Grimmy, and also for teaching me about a hidden builtin +5 bytes to fix two bugs Brute-force approach that's extremely slow, so obviously no TIO with test cases. Although TIO is too slow for the entire solution, I've added a ...

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