Ukrainian Mathematical Olympiad

Three boys picked nuts. After discovering that $420$ nuts are picked in total, the boys decided to share them evenly. First, one of the boys gave each of two others one fourth of the nuts he picked and a nut. Then another boy gave each of two others one fourth of the nuts he collected (those he picked and those he obtained from the first boy) and a nut. After the last boy had made this operation, it turned out that, indeed, the nuts were distributed evenly. Determine, how many nuts each boy picked.