Problem:
Score : 100 points

Problem Statement

There is a directed graph G with N vertices and M edges.
The vertices are numbered 1, 2, \ldots, N, and for each i (1 \leq i \leq M), the i-th directed edge goes from Vertex x_i to y_i.
G does not contain directed cycles.

Find the length of the longest directed path in G.
Here, the length of a directed path is the number of edges in it.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq x_i, y_i \leq N

All pairs (x_i, y_i) are distinct.

G does not contain directed cycles.

Input

Input is given from Standard Input in the following format:

N M
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the length of the longest directed path in G.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in Haskell (GHC 7.10.3) (judge verdict: Runtime Error)

{-# LANGUAGE BangPatterns #-}
import Control.Arrow
import Control.Monad.Fix
import Data.Int
import Data.Foldable
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.ByteString.Char8 as B
import Data.ByteString.Internal (accursedUnutterablePerformIO)
import Debug.Trace

unew :: VUM.Unbox a => Int -> VUM.IOVector a
unew !n = accursedUnutterablePerformIO $ VUM.unsafeNew n

uread :: VUM.Unbox a => Int -> VUM.IOVector a -> a
uread !i !v = accursedUnutterablePerformIO $ VUM.unsafeRead v i

uwrite :: VUM.Unbox a => Int -> a -> VUM.IOVector a -> VUM.IOVector a
uwrite !i !a !v =
  accursedUnutterablePerformIO $ VUM.unsafeWrite v i a >> return v

uthaw :: VUM.Unbox a => VU.Vector a -> VUM.IOVector a
uthaw !v = accursedUnutterablePerformIO $ VU.unsafeThaw v

ufreeze :: VUM.Unbox a => VUM.IOVector a -> VU.Vector a
ufreeze !v = accursedUnutterablePerformIO $ VU.unsafeFreeze v

uset :: VUM.Unbox a => a -> VUM.IOVector a -> VUM.IOVector a
uset !a !v = accursedUnutterablePerformIO $ VUM.set v a >> return v

solve :: Int -> Int -> VU.Vector (Int16, Int16) -> Int
solve n m edges = VU.maximum paths
 where
  graph :: V.Vector [Int16]
  graph = V.accumulate (\(!x) (!y) -> y : x)
                       (V.replicate n [])
                       (V.convert $ VU.map (first fromIntegral) edges)

  paths :: VU.Vector Int
  paths = ufreeze $ (\(_, !x) -> x) $ fix
    ( \(!f) (!i, !acc) ->
      if uread i acc >= 0
      then
        (i, acc)
      else
        let
          ts = graph V.! i
        in
          if null ts
          then
            (i, uwrite i 0 acc)
          else
            let
              acc' = foldl'
                (\(!acc) !t -> (\(_, !x) -> x) $ f (fromIntegral t, acc))
                acc
                ts
            in
              ( i
              , uwrite
                i
                (succ $ maximum $ map (\t -> uread (fromIntegral t) acc') ts)
                acc'
              )
    )
    (0, (uset (-1) $ unew n))

main = do
  let readInt :: Integral a => B.ByteString -> Maybe (a, B.ByteString)
      readInt = fmap (first fromIntegral . second B.tail) . B.readInt

  (n, m) <-
    (\vec -> (vec VU.! 0, vec VU.! 1)) . VU.unfoldrN 2 readInt <$> B.getLine
  edges <-
    VU.replicateM m
    $   (\vec -> (vec VU.! 0 - 1, vec VU.! 1 - 1))
    .   VU.unfoldrN 2 readInt
    <$> B.getLine
  print $ solve n m edges