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Line 1: {{Short description\|Mathematical function}} Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares aboutRandom stuff that no one cares about Random stuff that no one cares about Random stuff that no 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one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about Random stuff that no one cares about The definition of the '''BSDF''' ('''bidirectional scattering distribution function''') is not well standardized. The term was probably introduced in 1980 by Bartell, Dereniak, and Wolfe.<ref name=bartell1980>{{cite journal \|last1=~~Nicodemus~~Bartell▼ \|first1=F. EO.▼ \|last2=~~Richmond~~Dereniak▼ \|first2=JE. CL.▼ \|last3=~~Hsia~~Wolfe▼ \|first3=JW. JL.▼ \|editor-first1=Gary H. \|editor-last1=Hunt \|title=The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BTDF) \|volume=0257 \|url=http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1230783 \|publisher=Proceedings of SPIE Vol. 257 Radiation Scattering in Optical Systems \|accessdate=14 July 2014▼ \|pages=154–160 \|doi=10.1117/12.959611 \|year=1980\|series=Radiation Scattering in Optical Systems \|s2cid=128406154 \|url-access=subscription }} </ref> Most often it is used to name the general mathematical function which describes the way in which the light is scattered by a surface. However, in practice, this phenomenon is usually split into the reflected and transmitted components, which are then treated separately as '''BRDF''' ('''[[bidirectional reflectance distribution function]]''') and '''BTDF''' ('''bidirectional transmittance distribution function'''). [[Image:BSDF05 800.png\|thumb\|right\|280px\|BSDF: BRDF + BTDF]] * '''BSDF''' is a superset and the generalization of the '''BRDF''' and '''BTDF'''. The concept behind all BxDF functions could be described as a black box with the inputs being any two angles, one for incoming (incident) ray and the second one for the outgoing (reflected or transmitted) ray at a given point of the surface. The output of this black box is the value defining the ratio between the incoming and the outgoing light energy for the given couple of angles. The content of the black box may be a mathematical formula which more or less accurately tries to model and approximate the actual surface behavior or an algorithm which produces the output based on discrete samples of measured data. This implies that the function is 4(+1)-dimensional (4 values for 2 3D angles + 1 optional for wavelength of the light), which means that it cannot be simply represented by 2D and not even by a 3D graph. Each 2D or 3D graph, sometimes seen in the literature, shows only a slice of the function. * Some tend to use the term '''BSDF''' simply as a category name covering the whole family of BxDF functions. * The term '''BSDF''' is sometimes used in a slightly different context, for the function describing the amount of the scatter (not scattered light), simply as a function of the incident light angle. An example to illustrate this context: for perfectly [[Lambertian reflectance\|lambertian surface]] the BSDF (angle)=const. This approach is used for instance to verify the output quality by the manufacturers of the glossy surfaces.{{clarify\|date=November 2012}} * Another recent usage of the term '''BSDF''' can be seen in some 3D packages, when vendors use it as a 'smart' category to encompass the simple well known cg algorithms like [[Phong reflection model\|Phong]], [[Blinn–Phong reflection model\|Blinn–Phong]] etc. * Acquisition of the BSDF over the [[human face]] in 2000 by [[Paul Debevec\|Debevec]] et al.<ref name="Deb2000">{{cite book \| last = Debevec \| first = Paul \| authorlink = \| author2 = Tim Hawkins \| author3 = Chris Tchou \| author4 = Haarm-Pieter Duiker \| author5 = Westley Sarokin \| author6 = Mark Sagar \| chapter = Acquiring the reflectance field of a human face \| pages = 145–156 \| publisher = ACM \| year =~~1977}}~~ 2000▼ \| doi = 10.1145/344779.344855 \| title = Proceedings of the 27th annual conference on Computer graphics and interactive techniques - SIGGRAPH '00 \| isbn = 978-1581132083 \| s2cid = 2860203 }} </ref> was one of the last key breakthroughs on the way to fully [[virtual cinematography]] with its ultra-photorealistic [[digital look-alike]]s. The team was the first in the world to isolate the [[subsurface scattering]] component (a specialized case of BTDF) using the simplest [[light stage]], consisting on moveable light source, moveable high-res [[digital camera]], 2 [[polarizers]] in a few positions and really simple [[algorithm]]s on a modest [[computer]].<ref name="Deb2000"/> The team utilized the existing scientific knowledge that [[light]] that is reflected and scattered from the air-to-oil layer retains its [[Polarization (waves)\|polarization]] while light that travels within the [[skin]] loses its polarization.<ref name="Deb2000"/> The subsurface scattering component can be [[computer simulation\|simulated]] as a steady high-scatter glow of light from within the [[3D model\|model]]s, without which the skin does not look realistic. [[ESC Entertainment]], a company set up by [[Warner Brothers Pictures]] specially to do the visual effects / virtual cinematography system for [[The Matrix Reloaded]] and [[The Matrix Revolutions]] isolated the parameters for an approximate analytical BRDF which consisted of [[Lambertian diffusion]] component and a modified [[specular]] [[phong reflection model\|Phong]] component with a [[Fresnel equations\|Fresnel]] type of [[Visual effects\|effect]].<ref name="HaD2004">{{cite book \| last = Haber \| first = Jörg \| authorlink = \| author2 = Demetri Terzopoulos \| chapter = Facial modeling and animation \| pages = 6–es \| publisher = ACM \| year = 2004 \| doi = 10.1145/1103900.1103906 \| title = Proceedings of the conference on SIGGRAPH 2004 course notes - GRAPH '04 \| isbn = 978-0111456781 \| s2cid = 33684283 }}</ref> ==Overview of the BxDF functions== [[Image:BSSDF01 400.svg\|thumb\|right\|250px\|BRDF vs. BSSRDF]] * '''BRDF''' ('''[[Bidirectional reflectance distribution function]]''')<ref name="nicodemus1977">{{cite web\|last1=Nicodemus\|first1=F. E.\|last2=Richmond\|first2=J. C.\|last3=Hsia\|first3=J. J.\|last4=Ginsberg\|first4=I. W.\|last5=Limperis\|first5=T.\|year=1977\|title=Geometrical Considerations and Nomenclature for Reflectance\|url=http://graphics.stanford.edu/courses/cs448-05-winter/papers/nicodemus-brdf-nist.pdf\|publisher=Technical Report NBS MN-160, National Bureau of Standards\|accessdate=14 July 2014}} '''BSDF''' ('''Bidirectional scattering distribution function''') is the most general function.▼ '''BRDF''' ('''[[Bidirectional reflectance distribution function]]''')<~~ref name="nicodemus1977"~~/ref> is a simplified BSSRDF, assuming that light enters and leaves at the same point (''see the image on the right'').▼ '''BSSRDF''' ('''Bidirectional scattering-surface reflectance distribution function''' or '''B surface scattering RDF''')<ref name=nicodemus1977>{{cite web▼ ▲ \|last1=Nicodemus ▲ \|first1=F. E. ▲ \|last2=Richmond ▲ \|first2=J. C. ▲ \|last3=Hsia ▲ \|first3=J. J. ~~\|last4=Ginsberg~~ ~~\|first4=I. W.~~ ~~\|last5=Limperis~~ ~~\|first5=T.~~ ~~\|title=Geometrical Considerations and Nomenclature for Reflectance~~ ~~\|url=http://graphics.stanford.edu/courses/cs448-05-winter/papers/nicodemus-brdf-nist.pdf~~ ~~\|publisher=Technical Report NBS MN-160, National Bureau of Standards~~ ▲ \|accessdate=14 July 2014 ▲ \|year=1977}} </ref><ref name="jensen2001">{{cite book\|chapter-url=http://jbit.net/~sparky/bssrdf.pdf\|chapter=A Practical Model for Subsurface Light Transport\|last2=Marschner\|first2=S. R.\|year=2001\|website=graphics.ucsd.edu/~henrik/papers/bssrdf/\|publisher=Proceedings of ACM SIGGRAPH 2001\|pages=511–518\|doi=10.1145/383259.383319\|archive-url=\|archive-date=\|dead-url=\|last3=Levoy\|first3=M.\|last4=Hanrahan\|first4=P.\|last1=Jensen\|first1=H. W.\|title=Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH '01\|accessdate=14 July 2014\|isbn=978-1581133745\|citeseerx=10.1.1.503.7787}}</ref> describes the relation between outgoing radiance and the incident flux, including the phenomena like [[subsurface scattering]] (SSS). The BSSRDF describes how light is transported between any two rays that hit a surface. ▲'''BRDF''' ('''[[Bidirectional reflectance distribution function]]''')<ref name="nicodemus1977"/> is a simplified BSSRDF, assuming that light enters and leaves at the same point (''see the image on the right''). * '''BTDF''' ('''Bidirectional transmittance distribution function''')<ref name="bartell1980"/> is similar to BRDF but for the opposite side of the surface. (''see the top image''). ▲* '''~~BSDF~~BDF''' ('''Bidirectional ~~scattering~~ distribution function''') is ~~the~~collectively ~~most~~defined ~~general~~by ~~function~~BRDF and BTDF. * '''BSSRDF''' ('''Bidirectional scattering-surface reflectance distribution function''' or '''Bidirectional surface scattering RDF''')<ref name="nicodemus1977" /><ref name="jensen2001">{{cite book\|last1=Jensen\|first1=H. W.\|url=https://archive.org/details/siggraph2001conf00fium/page/511\|title=Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH '01\|last2=Marschner\|first2=S. R.\|last3=Levoy\|first3=M.\|last4=Hanrahan\|first4=P.\|website=graphics.ucsd.edu/~henrik/papers/bssrdf/\|publisher=Proceedings of ACM SIGGRAPH 2001\|year=2001\|isbn=978-1581133745\|pages=[https://archive.org/details/siggraph2001conf00fium/page/511 511–518]\|chapter=A Practical Model for Subsurface Light Transport\|citeseerx=10.1.1.503.7787\|doi=10.1145/383259.383319\|s2cid=11408331 \|chapter-url=http://jbit.net/~sparky/bssrdf.pdf\|accessdate=14 July 2014}}</ref> describes the relation between outgoing radiance and the incident flux, including the phenomena like [[subsurface scattering]] (SSS). The BSSRDF describes how light is transported between any two rays that hit a surface. ▲* '''~~BSSRDF~~BSSTDF''' ('''Bidirectional scattering-surface ~~reflectance~~transmittance distribution function''') oris ~~'''B~~like ~~surface~~BTDF ~~scattering~~but ~~RDF''')<ref~~with ~~name=nicodemus1977>{{cite~~subsurface ~~web~~scattering. * '''BSSDF''' ('''Bidirectional scattering-surface distribution function''') is collectively defined by BSSTDF and BSSRDF. Also known as '''BSDF''' ('''Bidirectional scattering distribution function'''). ==See also== ~~{{Portal\|Computer graphics}}~~ [[Bidirectional reflectance distribution function\|BRDF]] [[Radiometry]] Line 34 ⟶ 81: ==References== {{Reflist\|2}} ~~==External links==~~ [[Category:Radiometry]] <!--NB: Usage of term 'photometry' varies between astronomy and optics. The categories are named following the optics convention-->