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: Time Limit Exceeded)

import sys
sys.setrecursionlimit(10**9)
n,m = map(int,input().split())
graph = [[] for _ in range(n)]
for i in range(m):
  x,y = map(int,input().split())
  graph[x-1].append(y-1)
dp = [0]*(n)

done = []
def dfs(i):
    if i in done:
        done.pop()
        if dp[i] < len(done):dp[i] = len(done)
        return len(done)
    for j in graph[i]:
        if not(j in done):
            done.append(i)
            dfs(j)
    if dp[i] < len(done):dp[i] = len(done)
    if done:done.pop()
    return len(done)

for i in range(n):  
    dfs(i)
print(max(dp))