Problem:
Score : 100 points

Problem Statement

You are given a directed graph with N vertices and M edges, not necessarily simple. The i-th edge is oriented from the vertex a_i to the vertex b_i.
Divide this graph into strongly connected components and print them in their topological order.

Constraints

1 \leq N \leq 500,000

1 \leq M \leq 500,000

0 \leq a_i, b_i < N

Input

Input is given from Standard Input in the following format:

N M
a_0 b_0
a_1 b_1
:
a_{M - 1} b_{M - 1}

Output

Print 1+K lines, where K is the number of strongly connected components.
Print K on the first line.
Print the information of each strongly connected component in next K lines in the following format, where l is the number of vertices in the strongly connected component and v_i is the index of the vertex in it.

l v_0 v_1 ... v_{l-1}

Here, for each edge (a_i, b_i), b_i should not appear in earlier line than a_i.

If there are multiple correct output, print any of them.

Sample Input 1

6 7
1 4
5 2
3 0
5 5
4 1
0 3
4 2

Sample Output 1

4
1 5
2 4 1
1 2
2 3 0

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns, BinaryLiterals, CPP, DerivingStrategies  #-}
{-# LANGUAGE DerivingVia, FlexibleContexts, FlexibleInstances       #-}
{-# LANGUAGE GeneralizedNewtypeDeriving, KindSignatures, LambdaCase #-}
{-# LANGUAGE MagicHash, MultiParamTypeClasses, MultiWayIf           #-}
{-# LANGUAGE NumericUnderscores, OverloadedStrings, PatternSynonyms #-}
{-# LANGUAGE RankNTypes, RecordWildCards, ScopedTypeVariables       #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeApplications    #-}
{-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns  #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.Reader
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bifunctor
import           Data.Bool
import qualified Data.ByteString                   as B
import qualified Data.ByteString.Builder           as B
import qualified Data.ByteString.Char8             as C
import qualified Data.ByteString.Internal          as B
import qualified Data.ByteString.Unsafe            as B
import           Data.Char
import qualified Data.Foldable                     as F
import           Data.Function
import           Data.Functor.Identity
import qualified Data.IntMap.Strict                as IM
import qualified Data.IntSet                       as IS
import qualified Data.List                         as L
import qualified Data.Map.Strict                   as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive
import           Data.Proxy
import           Data.Ratio
import           Data.Semigroup
import qualified Data.Set                          as S
import           Data.Tuple
import qualified Data.Vector                       as V
import qualified Data.Vector.Algorithms.Intro      as Intro
import qualified Data.Vector.Fusion.Stream.Monadic as MS
import qualified Data.Vector.Fusion.Bundle.Monadic as MB
import           Data.Vector.Fusion.Util
import qualified Data.Vector.Generic               as G
import qualified Data.Vector.Generic.Mutable       as GM
import qualified Data.Vector.Mutable               as VM
import qualified Data.Vector.Primitive             as P
import qualified Data.Vector.Primitive.Mutable     as PM
import qualified Data.Vector.Unboxed               as U
import qualified Data.Vector.Unboxed.Mutable       as UM
import           Debug.Trace
import           Foreign                           hiding (void)
import           GHC.Exts
import           GHC.TypeLits
import           System.IO
import           Unsafe.Coerce

#define MOD 1000000007

main :: IO ()
main = do
    [n, m] <- map read.words <$> getLine
    es <- U.unfoldrN m (runParser $ (,) <$> int <*> int) <$> C.getContents
    let components = solve n m es
    print $ length components
    forM_ components $ \component -> do
        putStrLn.unwords.map show $ U.length component:U.toList component

solve :: Int -> Int -> U.Vector (Int, Int) -> [U.Vector Vertex]
solve n m es = stronglyConnectedComponents
    $ buildDirectedGraph n es

nothingSCC :: Int
nothingSCC = -1

stronglyConnectedComponents :: SparseGraph w -> [U.Vector Vertex]
stronglyConnectedComponents gr = runST $ do
    let numV = numVerticesCSR gr
    low <- UM.replicate numV nothingSCC
    preord <- UM.replicate numV nothingSCC
    stack <- newVecStack numV
    onStack <- UM.replicate numV False
    num <- newMutVar 0
    components <- newMutVar []

    rep numV $ \root -> do
        rootOrd <- UM.unsafeRead preord root
        when (rootOrd == nothingSCC) $ do
            flip fix root $ \dfs v -> do
                pord <- readMutVar num <* modifyMutVar' num (+1)
                UM.unsafeWrite preord v pord >> UM.unsafeWrite low v pord

                pushVS v stack >> UM.unsafeWrite onStack v True

                U.forM_ (adj gr v) $ \u -> do
                    isVisited <- (/= nothingSCC) <$> UM.unsafeRead preord u
                    if isVisited
                    then do
                        onS <- UM.unsafeRead onStack u
                        when onS $ do
                            uOrd <- UM.unsafeRead preord u
                            UM.unsafeModify low (min uOrd) v
                    else do
                        dfs u
                        uLow <- UM.unsafeRead low u
                        UM.unsafeModify low (min uLow) v

                isRoot <- (==)
                    <$> UM.unsafeRead low v
                    <*> UM.unsafeRead preord v
                when isRoot $ do
                    flip fix 1 $ \loop !i -> do
                        popVS stack >>= \case
                            Just x
                                | x /= v -> loop (i + 1)
                                | otherwise -> do
                                    o <- UM.unsafeRead (intVarsVS stack) _sizeVS
                                    component <- U.freeze $ UM.slice o i (internalVecStack stack)
                                    U.mapM_ (flip (UM.unsafeWrite onStack) False) component
                                    modifyMutVar' components (component:)
                            Nothing -> undefined
    readMutVar components


-------------------------------------------------------------------------------
-- Utils
-------------------------------------------------------------------------------
rep :: (Monad m) => Int -> (Int -> m ()) -> m ()
rep n = flip MS.mapM_ (stream 0 n)
{-# INLINE rep #-}
rev :: (Monad m) => Int -> (Int -> m ()) -> m ()
rev !n = flip MS.mapM_ (streamR 0 n)
{-# INLINE rev #-}
stream :: (Monad m) => Int -> Int -> MS.Stream m Int
stream !l !r = MS.Stream step l where { step x | x < r = return $ MS.Yield x (x + 1) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] stream #-}
streamR :: (Monad m) => Int -> Int -> MS.Stream m Int
streamR !l !r = MS.Stream step (r - 1) where { step x | x >= l = return $ MS.Yield x (x - 1) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] streamR #-}
stream' :: (Monad m) => Int -> Int -> Int -> MS.Stream m Int
stream' !l !r !d = MS.Stream step l where { step x | x < r = return $ MS.Yield x (x + d) | otherwise = return MS.Done; {-# INLINE [0] step #-}}
{-# INLINE [1] stream' #-}
infixl 8 `shiftRL`, `unsafeShiftRL`
shiftRL :: Int -> Int -> Int
shiftRL = unsafeShiftRL
{-# INLINE shiftRL #-}
unsafeShiftRL :: Int -> Int -> Int
unsafeShiftRL (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE unsafeShiftRL #-}
type Parser a = StateT C.ByteString Maybe a
runParser :: Parser a -> C.ByteString -> Maybe (a, C.ByteString)
runParser = runStateT
{-# INLINE runParser #-}
int :: Parser Int
int = coerce $ C.readInt . C.dropWhile isSpace
{-# INLINE int #-}
int1 :: Parser Int
int1 = fmap (subtract 1) int
{-# INLINE int1 #-}
char :: Parser Char
char = coerce C.uncons
{-# INLINE char #-}
byte :: Parser Word8
byte = coerce B.uncons
{-# INLINE byte #-}
skipSpaces :: Parser ()
skipSpaces = modify' (C.dropWhile isSpace)
{-# INLINE skipSpaces #-}
lowerBoundM :: (Monad m) => Int -> Int -> (Int -> m Bool) -> m Int
lowerBoundM low high p = go low high where { go !low !high | high <= low = return high | otherwise = p mid >>= bool (go (mid + 1) high) (go low mid) where { mid = low + unsafeShiftRL (high - low) 1}}
{-# INLINE lowerBoundM #-}
upperBoundM :: (Monad m) => Int -> Int -> (Int -> m Bool) -> m Int
upperBoundM low high p = do { flg <- p high; if flg then return high else subtract 1 <$!> lowerBoundM low high (fmap not . p)}
{-# INLINE upperBoundM #-}
lowerBound :: Int -> Int -> (Int -> Bool) -> Int
lowerBound low high p = runIdentity (lowerBoundM low high (return . p))
{-# INLINE lowerBound #-}
upperBound :: Int -> Int -> (Int -> Bool) -> Int
upperBound low high p = runIdentity (upperBoundM low high (return . p))
{-# INLINE upperBound #-}
-------------------------------------------------------------------------------
-- Data.VecQueue
-------------------------------------------------------------------------------
data VecQueue s a = VecQueue{intVarsVQ :: !(UM.MVector s Int), internalVecQueue :: !(UM.MVector s a)}
_dequeueCount :: Int
_dequeueCount = 0
{-# INLINE _dequeueCount #-}
_enqueueCount :: Int
_enqueueCount = 1
{-# INLINE _enqueueCount #-}
newVecQueue :: (PrimMonad m, UM.Unbox a) => Int -> m (VecQueue (PrimState m) a)
newVecQueue n = VecQueue <$> UM.replicate 2 0 <*> UM.unsafeNew n
defaultVecQueueSize :: Int
defaultVecQueueSize = 1024 * 1024
lengthVQ :: (PrimMonad m, UM.Unbox a) => VecQueue (PrimState m) a -> m Int
lengthVQ (VecQueue info _) = (-) <$> UM.unsafeRead info _enqueueCount <*> UM.unsafeRead info _dequeueCount
{-# INLINE lengthVQ #-}
dequeueVQ :: (PrimMonad m, UM.Unbox a) => VecQueue (PrimState m) a -> m (Maybe a)
dequeueVQ (VecQueue info q) = do { f <- UM.unsafeRead info _dequeueCount; r <- UM.unsafeRead info _enqueueCount; if f < r then do { UM.unsafeWrite info _dequeueCount (f + 1); pure <$> UM.unsafeRead q f} else return Nothing}
{-# INLINE dequeueVQ #-}
enqueueVQ :: (PrimMonad m, UM.Unbox a) => a -> VecQueue (PrimState m) a -> m ()
enqueueVQ x (VecQueue info q) = do { r <- UM.unsafeRead info _enqueueCount; UM.unsafeWrite q r x; UM.unsafeWrite info _enqueueCount (r + 1)}
{-# INLINE enqueueVQ #-}
enqueuesVQ :: (PrimMonad m, UM.Unbox a) => U.Vector a -> VecQueue (PrimState m) a -> m ()
enqueuesVQ vec (VecQueue info q) = do { r <- UM.unsafeRead info _enqueueCount; UM.unsafeWrite info _enqueueCount (r + U.length vec); U.unsafeCopy (UM.unsafeSlice r (U.length vec) q) vec}
{-# INLINE enqueuesVQ #-}
clearVQ :: (UM.Unbox a, PrimMonad m) => VecQueue (PrimState m) a -> m ()
clearVQ (VecQueue info _) = do { UM.unsafeWrite info _dequeueCount 0; UM.unsafeWrite info _enqueueCount 0}
freezeVecQueue :: (PrimMonad m, UM.Unbox a) => VecQueue (PrimState m) a -> m (U.Vector a)
freezeVecQueue (VecQueue info q) = do { f <- UM.unsafeRead info _dequeueCount; r <- UM.unsafeRead info _enqueueCount; U.unsafeFreeze $ UM.unsafeSlice f (r - f) q}
-------------------------------------------------------------------------------
-- Data.VecStack
-------------------------------------------------------------------------------
data VecStack s a = VecStack{intVarsVS :: !(UM.MVector s Int), internalVecStack :: !(UM.MVector s a)}
_sizeVS :: Int
_sizeVS = 0
{-# INLINE _sizeVS #-}
newVecStack :: (PrimMonad m, UM.Unbox a) => Int -> m (VecStack (PrimState m) a)
newVecStack n = VecStack <$> UM.replicate 1 0 <*> UM.unsafeNew n
defaultVecStackSize :: Int
defaultVecStackSize = 1024 * 1024
popVS :: (PrimMonad m, UM.Unbox a) => VecStack (PrimState m) a -> m (Maybe a)
popVS (VecStack info s) = do { len <- UM.unsafeRead info _sizeVS; if len > 0 then do { UM.unsafeWrite info _sizeVS (len - 1); pure <$> UM.unsafeRead s (len - 1)} else return Nothing}
{-# INLINE popVS #-}
pushVS :: (PrimMonad m, UM.Unbox a) => a -> VecStack (PrimState m) a -> m ()
pushVS x (VecStack info s) = do { len <- UM.unsafeRead info _sizeVS; UM.unsafeWrite s len x; UM.unsafeWrite info _sizeVS (len + 1)}
{-# INLINE pushVS #-}
pushesVS :: (PrimMonad m, UM.Unbox a) => U.Vector a -> VecStack (PrimState m) a -> m ()
pushesVS vec (VecStack info s) = do { len <- UM.unsafeRead info _sizeVS; UM.unsafeWrite info _sizeVS (len + U.length vec); U.unsafeCopy (UM.unsafeSlice len (U.length vec) s) vec}
{-# INLINE pushesVS #-}
freezeVecStack :: (PrimMonad m, U.Unbox a) => VecStack (PrimState m) a -> m (U.Vector a)
freezeVecStack (VecStack info s) = do { l <- UM.unsafeRead info _sizeVS; U.unsafeFreeze $ UM.take l s}
{-# INLINE freezeVecStack #-}
-------------------------------------------------------------------------------
-- Data.Graph.Sparse
-------------------------------------------------------------------------------
type Vertex = Int
type Edge = (Vertex, Vertex)
type EdgeWith w = (Vertex, Vertex, w)
type EdgeId = Int
data SparseGraph w = CSR{numVerticesCSR :: !Int, numEdgesCSR :: !Int, offsetCSR :: !(U.Vector Int), adjacentCSR :: !(U.Vector Vertex), edgeCtxCSR :: !(U.Vector w)}
data SparseGraphBuilder s w = SparseGraphBuilder{numVerticesSGB :: !Int, queueSGB :: VecQueue s (EdgeWith w), outDegSGB :: UM.MVector s Int}
buildSparseGraph :: (U.Unbox w) => Int -> (forall s . SparseGraphBuilder s w -> ST s ()) -> SparseGraph w
buildSparseGraph numVerticesCSR run = runST $ do { queueSGB <- newVecQueue (1024 * 1024); outDegSGB <- UM.replicate numVerticesCSR 0; run SparseGraphBuilder{numVerticesSGB = numVerticesCSR, ..}; numEdgesCSR <- lengthVQ queueSGB; offsetCSR <- U.scanl' (+) 0 <$> U.unsafeFreeze outDegSGB; moffset <- U.thaw offsetCSR; madj <- UM.unsafeNew numEdgesCSR; mectx <- UM.unsafeNew numEdgesCSR; edges <- freezeVecQueue queueSGB; U.forM_ edges $ \ (src, dst, w) -> do { pos <- UM.unsafeRead moffset src; UM.unsafeWrite moffset src (pos + 1); UM.unsafeWrite madj pos dst; UM.unsafeWrite mectx pos w}; adjacentCSR <- U.unsafeFreeze madj; edgeCtxCSR <- U.unsafeFreeze mectx; return CSR{..}}
{-# INLINE buildSparseGraph #-}
addDirectedEdge :: (U.Unbox w, PrimMonad m) => SparseGraphBuilder (PrimState m) w -> EdgeWith w -> m ()
addDirectedEdge SparseGraphBuilder{..} (src, dst, w) = do { enqueueVQ (src, dst, w) queueSGB; UM.unsafeModify outDegSGB (+ 1) src}
{-# INLINE addDirectedEdge #-}
addUndirectedEdge :: (U.Unbox w, PrimMonad m) => SparseGraphBuilder (PrimState m) w -> EdgeWith w -> m ()
addUndirectedEdge SparseGraphBuilder{..} (src, dst, w) = do { enqueueVQ (src, dst, w) queueSGB; enqueueVQ (dst, src, w) queueSGB; UM.unsafeModify outDegSGB (+ 1) src; UM.unsafeModify outDegSGB (+ 1) dst}
{-# INLINE addUndirectedEdge #-}
addDirectedEdge_ :: (PrimMonad m) => SparseGraphBuilder (PrimState m) () -> Edge -> m ()
addDirectedEdge_ SparseGraphBuilder{..} (src, dst) = do { enqueueVQ (src, dst, ()) queueSGB; UM.unsafeModify outDegSGB (+ 1) src}
{-# INLINE addDirectedEdge_ #-}
addUndirectedEdge_ :: (PrimMonad m) => SparseGraphBuilder (PrimState m) () -> Edge -> m ()
addUndirectedEdge_ SparseGraphBuilder{..} (src, dst) = do { enqueueVQ (src, dst, ()) queueSGB; enqueueVQ (dst, src, ()) queueSGB; UM.unsafeModify outDegSGB (+ 1) src; UM.unsafeModify outDegSGB (+ 1) dst}
{-# INLINE addUndirectedEdge_ #-}
buildDirectedGraph :: Int -> U.Vector Edge -> SparseGraph ()
buildDirectedGraph numVerticesCSR edges = buildSparseGraph numVerticesCSR $ \ builder -> do { U.mapM_ (addDirectedEdge_ builder) edges}
buildUndirectedGraph :: Int -> U.Vector Edge -> SparseGraph ()
buildUndirectedGraph numVerticesCSR edges = buildSparseGraph numVerticesCSR $ \ builder -> do { U.mapM_ (addUndirectedEdge_ builder) edges}
buildDirectedGraphW :: (U.Unbox w) => Int -> U.Vector (EdgeWith w) -> SparseGraph w
buildDirectedGraphW numVerticesCSR edges = buildSparseGraph numVerticesCSR $ \ builder -> do { U.mapM_ (addDirectedEdge builder) edges}
buildUndirectedGraphW :: (U.Unbox w) => Int -> U.Vector (EdgeWith w) -> SparseGraph w
buildUndirectedGraphW numVerticesCSR edges = buildSparseGraph numVerticesCSR $ \ builder -> do { U.mapM_ (addUndirectedEdge builder) edges}
adj :: SparseGraph w -> Vertex -> U.Vector Vertex
adj CSR{..} v = U.unsafeSlice o (o' - o) adjacentCSR where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE adj #-}
iadj :: SparseGraph w -> Vertex -> U.Vector (EdgeId, Vertex)
iadj CSR{..} v = U.imap ((,) . (+ o)) $ U.unsafeSlice o (o' - o) adjacentCSR where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE iadj #-}
adjW :: (U.Unbox w) => SparseGraph w -> Vertex -> U.Vector (Vertex, w)
adjW CSR{..} v = U.zip (U.unsafeSlice o (o' - o) adjacentCSR) (U.unsafeSlice o (o' - o) edgeCtxCSR) where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE adjW #-}
iadjW :: (U.Unbox w) => SparseGraph w -> Vertex -> U.Vector (EdgeId, Vertex, w)
iadjW CSR{..} v = U.izipWith (\ i u w -> (i + o, u, w)) (U.unsafeSlice o (o' - o) adjacentCSR) (U.unsafeSlice o (o' - o) edgeCtxCSR) where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE iadjW #-}
outEdges :: SparseGraph w -> Vertex -> U.Vector EdgeId
outEdges CSR{..} v = U.generate (o' - o) (+ o) where { o = U.unsafeIndex offsetCSR v; o' = U.unsafeIndex offsetCSR (v + 1)}
{-# INLINE outEdges #-}
outDegree :: SparseGraph w -> Vertex -> Int
outDegree CSR{..} v = U.unsafeIndex offsetCSR (v + 1) - U.unsafeIndex offsetCSR v
{-# INLINE outDegree #-}
outDegrees :: SparseGraph w -> U.Vector Int
outDegrees CSR{..} = U.zipWith (-) offsetCSR $ U.tail offsetCSR
{-# INLINE outDegrees #-}