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 Python (3.4.3) (judge verdict: Accepted)

#topological sort
from collections import deque,defaultdict
#n:ノードの数　m:エッジ辺の数
n,m=map(int,input().split())
#m個の有向辺　xi -> yi
edges=[tuple(map(int,input().split())) for i in range(m)]

in_cnt=defaultdict(int) #i番目のノードの入力辺の数
outs=defaultdict(list) #i番目のノードからi0,i1,i2,・・・番目のノードに辺が存在する時outs{i:[i0,i1,i2・・・]}

for out_node,in_node in edges:
    in_cnt[in_node-1]+=1
    outs[out_node-1].append(in_node-1)

topo_sort=[] #ソートされた結果を代入する
q=deque([i for i in range(n) if in_cnt[i]==0]) #入力の存在しないノードを入れる

dp=[0]*n
while q:
    v1=q.popleft()
    topo_sort.append(v1)
    for v2 in outs[v1]:
        in_cnt[v2]-=1
        dp[v2]=dp[v1]+1
        if in_cnt[v2]==0:
            q.append(v2)
print(max(dp))