import qualified Data.IntMap as I
import Control.Monad
import Data.List
import Data.Maybe
import System.Random
 
main :: IO ()
main = do
  rd <- replicateM 100000 rollIkasamaDice
  let im  = foldr (I.update ((Just $!) . succ)) im0 rd
      im0 = I.fromList $ zip [1..4] [0,0..]
  print im
 
rollIkasamaDice :: IO Int
rollIkasamaDice = do
  d <- getStdRandom (randomR (0, 1)) :: IO Double
  let thr = scanl1 (+) $ map . flip (/) =<< sum $ map sqrt [1..4]
      a   = zip thr [1..] :: [(Double, Int)]
 
  return $ snd $ fromJust $ find ((d <=) . fst) a
 

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