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: Accepted)

{-# LANGUAGE BangPatterns #-}
{-
G - Longest Path

問題文

N頂点 M 辺の有向グラフ G があります。
頂点には 1,2,…,N と番号が振られています。
各 i (1≤i≤M) について、i 番目の有向辺は頂点 xi から yi へ張られています。
Gは有向閉路を含みません。

Gの有向パスのうち、最長のものの長さを求めてください。
ただし、有向パスの長さとは、有向パスに含まれる辺の本数のことです。

制約
    入力はすべて整数である。
    2≤ N ≤10^5
    1≤ M ≤10^5
    1≤ xi,yi ≤N
    ペア (xi,yi)はすべて相異なる。
    Gは有向閉路を含まない。

入力

入力は以下の形式で標準入力から与えられる。

N M
x1 y1
x2 y2
:
xM yM

出力

Gの有向パスのうち、最長のものの長さを出力せよ。
-}

import qualified Data.ByteString.Char8 as B
import Control.Monad
import Data.List
import qualified Data.Vector.Unboxed as UV
import qualified Data.Vector.Unboxed.Mutable as MV
import Control.Monad.ST
import qualified Data.Map.Strict as M

t2 [a,b]=(a-1,b-1)
main=do
    [n,m] <- map read.words<$>getLine
    xys <- replicateM m $ t2.unfoldr (B.readInt.B.dropWhile(<'!'))<$>B.getLine
    print $ UV.maximum $ f n m $ grp xys

grp = foldl' ad M.empty where
    ad m (x,y) = M.alter (al y) x m
    al y Nothing = Just [y]
    al y (Just l) = Just (y:l)

f n m !xys = runST $ do
    dp <- MV.replicate n (-1) :: ST s (MV.STVector s Int)
    forM_ [0..n-1] (dfs dp)
    UV.freeze dp
    where
        dfs dp s = do
            sk <- MV.read dp s
            if sk == (-1)
                then do
                    sm <- (+1).maximum.((-1):) <$> mapM (dfs dp) (nodes s)
                    MV.write dp s sm
                    return sm
                else
                    return sk
        nodes s = M.findWithDefault [] s xys