Juxtaposition of fmaps.

fmap.hs

-- 3
fmap fmap fmap
= fmap . fmap

-- 4
fmap fmap fmap fmap
= (fmap . fmap) fmap
= fmap (fmap fmap)

-- 5
fmap fmap fmap fmap fmap
= fmap (fmap fmap) fmap
= fmap fmap . fmap

-- 6
fmap fmap fmap fmap fmap fmap
= (fmap fmap . fmap) fmap
= fmap fmap (fmap fmap)
= fmap . fmap fmap
= \f -> fmap (fmap fmap f)
= \f -> fmap (fmap . f)
= fmap . (fmap .)

-- 7
fmap fmap fmap fmap fmap fmap fmap
= (fmap . (fmap .)) fmap
= fmap (fmap . fmap)

-- 8
fmap fmap fmap fmap fmap fmap fmap fmap
= fmap (fmap . fmap) fmap
= fmap . fmap . fmap

-- 9
fmap fmap fmap fmap fmap fmap fmap fmap fmap
= (fmap . fmap . fmap) fmap
= fmap (fmap (fmap fmap))

-- 10
fmap fmap fmap fmap fmap fmap fmap fmap fmap fmap
= fmap (fmap (fmap fmap)) fmap
= fmap (fmap fmap) . fmap
= \f -> fmap (fmap fmap) (fmap f)
= \f -> fmap fmap . fmap f
-- using 2nd functor law: fmap f . fmap g = fmap (f . g)
= \f -> fmap (fmap . f)
= fmap . (fmap .)
= fmap fmap fmap fmap fmap fmap -- 6

-- N >= 10
fmap fmap ... fmap    -- N times
= fmap fmap ... fmap  -- (N - 4) times