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 Fortran (gfortran v4.8.4) (judge verdict: Runtime Error)

integer N,M
integer X,Y
integer,allocatable,dimension(:,:)::EDGE
integer,allocatable,dimension(:)::Nindex
integer,allocatable,dimension(:)::DP
integer ans
!読み込み
read*,N,M
allocate(DP(N))
allocate(EDGE(N,M))
allocate(Nindex(N))
EDGE=0
Nindex=0
do i=1,M
  read*,X,Y
  Nindex(X)=Nindex(X)+1
  EDGE(X,Nindex(X))=Y
end do
!読み込み終了

DP = -1
!DP[i]とはノードiからのびる経路のうち最短のもの
!まだ調べていない状態は-1とする
ans = 0
do i=1,N
  if(DP(i)==-1)DP(i)=DFS(i)
  ans=max(ans,DP(i) )
end do

print"(I0)",ans

contains

recursive function DFS(u)result(res)
integer u,res
  if(DP(u) >= 0)then
    res=DP(u)
  else
    DP(u)=0
    do j=1,Nindex(u)
      DP(u)=max(DP(u),DFS(EDGE(u,j))+1)
    end do
  res=DP(u)
  endif
end function DFS
end