module Main where

import Bell
import Matchings
import Stirling
import Control.Monad

heightOfDistinctAtoms :: Int -> Integer
heightOfDistinctAtoms n = toInteger $ n + 1

heightOfAtoms :: Int -> Integer
heightOfAtoms n = sum [ norbits k * heightOfDistinctAtoms k | k <- [0 .. n] ]
                  + sum [ matchings o1 o2 | (o1, o2) <- cross ]
  where
    norbits k = secondStirling n k
    orbits k = replicate (fromIntegral (norbits k)) k
    allOrbits = concat [ orbits k | k <- [0..n] ]
    cross = [ (allOrbits !! i, allOrbits !! j) | let m = length allOrbits, i <- [0 .. m-1], j <- [i+1 .. m-1] ]

orbitsOf :: Int -> [Int]
orbitsOf n = concat [ replicate (fromIntegral (secondStirling n k)) k | k <- [0..n] ]

main :: IO ()
main = do
  let out = [ (i, heightOfAtoms i, bell (2*i)) | i <- [0..10] ]
  forM_ out $ \(i, n, b) -> putStrLn ("h(A^" ++ show i ++ ") = " ++ show n ++ "   <   B_" ++ show (2*i) ++ " = " ++ show b)