!YS-v0

defn main(*inputs):
  each input inputs: !:say
    apply format '%s, %s, (%d)':
      best-shuffle(input)

defn best-shuffle(s):
  ref =: s:group-indices:cycles
  prm =: concat.apply(map(partial(rotate 1) ref))
  ref =: concat(ref*)

  map(vector ref prm):
    .sort-by(first _)
    .map(second)
    .map(partial(get s))
    .str(*)
    .call(\([s _ s.score(_)]) _)

defn score(before after):
  map(== before after)
    .filter(true?).#

defn group-indices(s):
  map-indexed(vector s)
    .merge-vecs({}):vals
    .sort-by(count _):reverse

defn cycles(coll):
  n =: coll.0.#
  cycle =: range(n):cycle
  coll =: concat(coll*)
  map(vector coll cycle):
    .merge-vecs([])

defn rotate(n coll):
  c =: coll.#
  n =: (c + n) % c
  concat coll.drop(n): coll.take(n)

defn merge-vecs(vecs init):
  reduce _ init vecs:
    fn(counts [index x]):
      assoc counts x:
        counts.$x.or([]).conj(index)