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Mu.hs
-- | For reference, see http://en.wikipedia.org/wiki/MU_puzzle.
module Main where
import Control.Monad ((>=>))
import Data.Maybe (mapMaybe)
-- | The base language primitives.
data MuVal = U | I | M deriving (Show, Eq)
-- | Names for the MU rules.
data MuRule = R1 | R2 | R3 | R4 deriving (Show, Eq, Ord)
-- | A string of the primitives.
type MuString = [MuVal]
-- | The type of the 4 rules in the language.
type Rule = (MuString -> Maybe MuString)
-- | Function to convert from a Rule name to a Rule function
ruleFn :: MuRule -> Rule
ruleFn R1 = rule1
ruleFn R2 = rule2
ruleFn R3 = rule3
ruleFn R4 = rule4
-- | Rule 1: Add a `U` to the end of any string ending in I.
-- For example: `MI` to `MIU`
rule1 :: MuString -> Maybe MuString
rule1 s = case reverse s of
(I:_) -> Just (s ++ [U])
_ -> Nothing
-- | Rule 2: Double the string after the `M` (that is, change `Mx`, to `Mxx`).
-- For example: `MIU` to `MIUIU`.
rule2 :: MuString -> Maybe MuString
rule2 s = case s of
(M:rst) -> Just $ [M] ++ rst ++ rst
_ -> Nothing
-- | Rule 3: Replicate `III` with a `U`.
-- For example: `MUIIIU` to `MUUU`.
rule3 :: MuString -> Maybe MuString
rule3 s = applyIfApplicable s r3
where
r3 (I:I:I:rs) = U : r3 rs
r3 (r:rs) = r : r3 rs
r3 [] = []
-- | Rule 4: Remove any `UU`.
-- For example: `MUUU` to `MU`.
rule4 :: MuString -> Maybe MuString
rule4 s = applyIfApplicable s r4
where
r4 (U:U:rs) = r4 rs
r4 (r:rs) = r : r4 rs
r4 [] = []
-- | Returns the result of applying `fn` to `s` if and only if the result of
-- `fn s` differs from `s`.
applyIfApplicable :: (Eq a) => a -> (a -> a) -> Maybe a
applyIfApplicable s fn = let s' = fn s
in if s == s'
then Nothing
else Just s'
-- | Accepts a string and a list of rules to apply to the string in order.
runRules :: MuString -> [Rule] -> Maybe MuString
runRules s [] = Just s
runRules s (r:rs) = foldl (>=>) r rs s
-- | Creates all possible combinations of list of values.
-- > take 10 $ sequences "ab"
-- ["a","b","aa","ab","ba","bb","aaa","aab","aba","abb"]
--
-- Note: Job Vranish helped me with this one a lot.
sequences :: [a] -> [[a]]
sequences ls = ls' ++ [i ++ [a] | i <- sequences ls, a <- ls]
where
ls' = map (:[]) ls
-- | Produce a show-your-work result from an initial string and a list of rules.
ruleResult :: MuString -> [MuRule] -> Maybe ([MuRule], MuString)
ruleResult s rs = let ruleFns = map ruleFn rs
in case runRules s ruleFns of
Just s' -> Just (rs, s')
Nothing -> Nothing
-- | Make a result into a something printable.
showRule :: ([MuRule], MuString) -> String
showRule (rs, s) = concat [ "By: "
, show rs
, "\n"
, "Found string: "
, show s
, "\n"
]
-- | Print out found strings seraching from the initial string of "MI"
main :: IO ()
main = mapM_ (putStrLn . showRule) $ mapMaybe (ruleResult initial) ruleSeqs
where
initial = [M,I]
ruleSeqs = sequences [R1,R2,R3,R4]
@sw17ch

sw17ch commented Feb 25, 2014

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Here's the output of this program when using an initial string of [M,I] and outputting 100 strings.

$ runhaskell Mu.hs
By: [R1]
Found string: [M,I,U]

By: [R2]
Found string: [M,I,I]

By: [R1,R2]
Found string: [M,I,U,I,U]

By: [R2,R1]
Found string: [M,I,I,U]

By: [R2,R2]
Found string: [M,I,I,I,I]

By: [R1,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U]

By: [R2,R1,R2]
Found string: [M,I,I,U,I,I,U]

By: [R2,R2,R1]
Found string: [M,I,I,I,I,U]

By: [R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I]

By: [R2,R2,R3]
Found string: [M,U,I]

By: [R1,R2,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U]

By: [R2,R1,R2,R2]
Found string: [M,I,I,U,I,I,U,I,I,U,I,I,U]

By: [R2,R2,R1,R2]
Found string: [M,I,I,I,I,U,I,I,I,I,U]

By: [R2,R2,R1,R3]
Found string: [M,U,I,U]

By: [R2,R2,R2,R1]
Found string: [M,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I]

By: [R2,R2,R2,R3]
Found string: [M,U,U,I,I]

By: [R2,R2,R3,R1]
Found string: [M,U,I,U]

By: [R2,R2,R3,R2]
Found string: [M,U,I,U,I]

By: [R1,R2,R2,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U]

By: [R2,R1,R2,R2,R2]
Found string: [M,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U]

By: [R2,R2,R1,R2,R2]
Found string: [M,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R3]
Found string: [M,U,I,U,U,I,U]

By: [R2,R2,R1,R3,R2]
Found string: [M,U,I,U,U,I,U]

By: [R2,R2,R2,R1,R2]
Found string: [M,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R1,R3]
Found string: [M,U,U,I,I,U]

By: [R2,R2,R2,R2,R1]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I]

By: [R2,R2,R2,R2,R3]
Found string: [M,U,U,U,U,U,I]

By: [R2,R2,R2,R3,R1]
Found string: [M,U,U,I,I,U]

By: [R2,R2,R2,R3,R2]
Found string: [M,U,U,I,I,U,U,I,I]

By: [R2,R2,R2,R3,R4]
Found string: [M,I,I]

By: [R2,R2,R3,R1,R2]
Found string: [M,U,I,U,U,I,U]

By: [R2,R2,R3,R2,R1]
Found string: [M,U,I,U,I,U]

By: [R2,R2,R3,R2,R2]
Found string: [M,U,I,U,I,U,I,U,I]

By: [R1,R2,R2,R2,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U]

By: [R2,R1,R2,R2,R2,R2]
Found string: [M,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U]

By: [R2,R2,R1,R2,R2,R2]
Found string: [M,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R2,R3]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R3,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R3,R4]
Found string: [M,U,I,I,U]

By: [R2,R2,R1,R3,R2,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R3,R2,R4]
Found string: [M,U,I,I,U]

By: [R2,R2,R2,R1,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R1,R2,R3]
Found string: [M,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R3,R2]
Found string: [M,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R3,R4]
Found string: [M,I,I,U]

By: [R2,R2,R2,R2,R1,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R1,R3]
Found string: [M,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R2,R1]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I]

By: [R2,R2,R2,R2,R2,R3]
Found string: [M,U,U,U,U,U,U,U,U,U,U,I,I]

By: [R2,R2,R2,R2,R3,R1]
Found string: [M,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R3,R2]
Found string: [M,U,U,U,U,U,I,U,U,U,U,U,I]

By: [R2,R2,R2,R2,R3,R4]
Found string: [M,U,I]

By: [R2,R2,R2,R3,R1,R2]
Found string: [M,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R3,R1,R4]
Found string: [M,I,I,U]

By: [R2,R2,R2,R3,R2,R1]
Found string: [M,U,U,I,I,U,U,I,I,U]

By: [R2,R2,R2,R3,R2,R2]
Found string: [M,U,U,I,I,U,U,I,I,U,U,I,I,U,U,I,I]

By: [R2,R2,R2,R3,R2,R4]
Found string: [M,I,I,I,I]

By: [R2,R2,R2,R3,R4,R1]
Found string: [M,I,I,U]

By: [R2,R2,R2,R3,R4,R2]
Found string: [M,I,I,I,I]

By: [R2,R2,R3,R1,R2,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R3,R1,R2,R4]
Found string: [M,U,I,I,U]

By: [R2,R2,R3,R2,R1,R2]
Found string: [M,U,I,U,I,U,U,I,U,I,U]

By: [R2,R2,R3,R2,R2,R1]
Found string: [M,U,I,U,I,U,I,U,I,U]

By: [R2,R2,R3,R2,R2,R2]
Found string: [M,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I]

By: [R1,R2,R2,R2,R2,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U]

By: [R2,R1,R2,R2,R2,R2,R2]
Found string: [M,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U]

By: [R2,R2,R1,R2,R2,R2,R2]
Found string: [M,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R2,R2,R3]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R2,R3,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R2,R3,R4]
Found string: [M,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R3,R2,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R3,R2,R4]
Found string: [M,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R3,R4,R2]
Found string: [M,U,I,I,U,U,I,I,U]

By: [R2,R2,R1,R3,R2,R2,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R3,R2,R2,R4]
Found string: [M,U,I,I,I,I,U]

By: [R2,R2,R1,R3,R2,R4,R2]
Found string: [M,U,I,I,U,U,I,I,U]

By: [R2,R2,R2,R1,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R1,R2,R2,R3]
Found string: [M,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R2,R3,R2]
Found string: [M,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R2,R3,R4]
Found string: [M,I,I,U,I,I,U]

By: [R2,R2,R2,R1,R3,R2,R2]
Found string: [M,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R3,R2,R4]
Found string: [M,I,I,U,I,I,U]

By: [R2,R2,R2,R1,R3,R4,R2]
Found string: [M,I,I,U,I,I,U]

By: [R2,R2,R2,R2,R1,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R1,R2,R3]
Found string: [M,U,U,U,U,U,I,U,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R1,R3,R2]
Found string: [M,U,U,U,U,U,I,U,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R1,R3,R4]
Found string: [M,U,I,U]

By: [R2,R2,R2,R2,R2,R1,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R2,R1,R3]
Found string: [M,U,U,U,U,U,U,U,U,U,U,I,I,U]

By: [R2,R2,R2,R2,R2,R2,R1]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I]

By: [R2,R2,R2,R2,R2,R2,R3]
Found string: [M,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,I]

By: [R2,R2,R2,R2,R2,R3,R1]
Found string: [M,U,U,U,U,U,U,U,U,U,U,I,I,U]

By: [R2,R2,R2,R2,R2,R3,R2]
Found string: [M,U,U,U,U,U,U,U,U,U,U,I,I,U,U,U,U,U,U,U,U,U,U,I,I]

By: [R2,R2,R2,R2,R2,R3,R4]
Found string: [M,I,I]

By: [R2,R2,R2,R2,R3,R1,R2]
Found string: [M,U,U,U,U,U,I,U,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R3,R1,R4]
Found string: [M,U,I,U]

CornSyrup:~ runhaskell Mu.hs
By: [R1]
Found string: [M,I,U]

By: [R2]
Found string: [M,I,I]

By: [R1,R2]
Found string: [M,I,U,I,U]

By: [R2,R1]
Found string: [M,I,I,U]

By: [R2,R2]
Found string: [M,I,I,I,I]

By: [R1,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U]

By: [R2,R1,R2]
Found string: [M,I,I,U,I,I,U]

By: [R2,R2,R1]
Found string: [M,I,I,I,I,U]

By: [R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I]

By: [R2,R2,R3]
Found string: [M,U,I]

By: [R1,R2,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U]

By: [R2,R1,R2,R2]
Found string: [M,I,I,U,I,I,U,I,I,U,I,I,U]

By: [R2,R2,R1,R2]
Found string: [M,I,I,I,I,U,I,I,I,I,U]

By: [R2,R2,R1,R3]
Found string: [M,U,I,U]

By: [R2,R2,R2,R1]
Found string: [M,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I]

By: [R2,R2,R2,R3]
Found string: [M,U,U,I,I]

By: [R2,R2,R3,R1]
Found string: [M,U,I,U]

By: [R2,R2,R3,R2]
Found string: [M,U,I,U,I]

By: [R1,R2,R2,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U]

By: [R2,R1,R2,R2,R2]
Found string: [M,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U]

By: [R2,R2,R1,R2,R2]
Found string: [M,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R3]
Found string: [M,U,I,U,U,I,U]

By: [R2,R2,R1,R3,R2]
Found string: [M,U,I,U,U,I,U]

By: [R2,R2,R2,R1,R2]
Found string: [M,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R1,R3]
Found string: [M,U,U,I,I,U]

By: [R2,R2,R2,R2,R1]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I]

By: [R2,R2,R2,R2,R3]
Found string: [M,U,U,U,U,U,I]

By: [R2,R2,R2,R3,R1]
Found string: [M,U,U,I,I,U]

By: [R2,R2,R2,R3,R2]
Found string: [M,U,U,I,I,U,U,I,I]

By: [R2,R2,R2,R3,R4]
Found string: [M,I,I]

By: [R2,R2,R3,R1,R2]
Found string: [M,U,I,U,U,I,U]

By: [R2,R2,R3,R2,R1]
Found string: [M,U,I,U,I,U]

By: [R2,R2,R3,R2,R2]
Found string: [M,U,I,U,I,U,I,U,I]

By: [R1,R2,R2,R2,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U]

By: [R2,R1,R2,R2,R2,R2]
Found string: [M,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U]

By: [R2,R2,R1,R2,R2,R2]
Found string: [M,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R2,R3]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R3,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R3,R4]
Found string: [M,U,I,I,U]

By: [R2,R2,R1,R3,R2,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R3,R2,R4]
Found string: [M,U,I,I,U]

By: [R2,R2,R2,R1,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R1,R2,R3]
Found string: [M,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R3,R2]
Found string: [M,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R3,R4]
Found string: [M,I,I,U]

By: [R2,R2,R2,R2,R1,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R1,R3]
Found string: [M,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R2,R1]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I]

By: [R2,R2,R2,R2,R2,R3]
Found string: [M,U,U,U,U,U,U,U,U,U,U,I,I]

By: [R2,R2,R2,R2,R3,R1]
Found string: [M,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R3,R2]
Found string: [M,U,U,U,U,U,I,U,U,U,U,U,I]

By: [R2,R2,R2,R2,R3,R4]
Found string: [M,U,I]

By: [R2,R2,R2,R3,R1,R2]
Found string: [M,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R3,R1,R4]
Found string: [M,I,I,U]

By: [R2,R2,R2,R3,R2,R1]
Found string: [M,U,U,I,I,U,U,I,I,U]

By: [R2,R2,R2,R3,R2,R2]
Found string: [M,U,U,I,I,U,U,I,I,U,U,I,I,U,U,I,I]

By: [R2,R2,R2,R3,R2,R4]
Found string: [M,I,I,I,I]

By: [R2,R2,R2,R3,R4,R1]
Found string: [M,I,I,U]

By: [R2,R2,R2,R3,R4,R2]
Found string: [M,I,I,I,I]

By: [R2,R2,R3,R1,R2,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R3,R1,R2,R4]
Found string: [M,U,I,I,U]

By: [R2,R2,R3,R2,R1,R2]
Found string: [M,U,I,U,I,U,U,I,U,I,U]

By: [R2,R2,R3,R2,R2,R1]
Found string: [M,U,I,U,I,U,I,U,I,U]

By: [R2,R2,R3,R2,R2,R2]
Found string: [M,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I]

By: [R1,R2,R2,R2,R2,R2,R2]
Found string: [M,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U,I,U]

By: [R2,R1,R2,R2,R2,R2,R2]
Found string: [M,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U,I,I,U]

By: [R2,R2,R1,R2,R2,R2,R2]
Found string: [M,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R2,R2,R3]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R2,R3,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R2,R3,R4]
Found string: [M,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R3,R2,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R2,R3,R2,R4]
Found string: [M,U,I,I,I,I,U]

By: [R2,R2,R1,R2,R3,R4,R2]
Found string: [M,U,I,I,U,U,I,I,U]

By: [R2,R2,R1,R3,R2,R2,R2]
Found string: [M,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U,U,I,U]

By: [R2,R2,R1,R3,R2,R2,R4]
Found string: [M,U,I,I,I,I,U]

By: [R2,R2,R1,R3,R2,R4,R2]
Found string: [M,U,I,I,U,U,I,I,U]

By: [R2,R2,R2,R1,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R1,R2,R2,R3]
Found string: [M,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R2,R3,R2]
Found string: [M,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R2,R3,R4]
Found string: [M,I,I,U,I,I,U]

By: [R2,R2,R2,R1,R3,R2,R2]
Found string: [M,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U,U,U,I,I,U]

By: [R2,R2,R2,R1,R3,R2,R4]
Found string: [M,I,I,U,I,I,U]

By: [R2,R2,R2,R1,R3,R4,R2]
Found string: [M,I,I,U,I,I,U]

By: [R2,R2,R2,R2,R1,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R1,R2,R3]
Found string: [M,U,U,U,U,U,I,U,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R1,R3,R2]
Found string: [M,U,U,U,U,U,I,U,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R1,R3,R4]
Found string: [M,U,I,U]

By: [R2,R2,R2,R2,R2,R1,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R2,R1,R3]
Found string: [M,U,U,U,U,U,U,U,U,U,U,I,I,U]

By: [R2,R2,R2,R2,R2,R2,R1]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,U]

By: [R2,R2,R2,R2,R2,R2,R2]
Found string: [M,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I,I]

By: [R2,R2,R2,R2,R2,R2,R3]
Found string: [M,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,U,I]

By: [R2,R2,R2,R2,R2,R3,R1]
Found string: [M,U,U,U,U,U,U,U,U,U,U,I,I,U]

By: [R2,R2,R2,R2,R2,R3,R2]
Found string: [M,U,U,U,U,U,U,U,U,U,U,I,I,U,U,U,U,U,U,U,U,U,U,I,I]

By: [R2,R2,R2,R2,R2,R3,R4]
Found string: [M,I,I]

By: [R2,R2,R2,R2,R3,R1,R2]
Found string: [M,U,U,U,U,U,I,U,U,U,U,U,U,I,U]

By: [R2,R2,R2,R2,R3,R1,R4]
Found string: [M,U,I,U]

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