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: Wrong Answer)

import numpy as np

N,M = map(int, input().split())
t_table = {}
for i in range(M):
	x,y = map(int, input().split())
	if x-1 in t_table: t_table[x-1].append(y-1)
	else: t_table[x-1] = [y-1]
mem = np.zeros(N, dtype='int32')
ans = 0
ccheck = [True for _ in range(N)]
NodeList = np.array([i for i in range(N)])
while True:
	p_mem = mem.copy()
	p_cnt = np.zeros(N, dtype='int32')
	for i in NodeList[ccheck]:
		if i in t_table :
			p_cnt[t_table[i]] = 1
	mem+=p_cnt
	ccheck = (mem!=p_mem)
	if((mem==p_mem).all()):
	 	print(ans)
	 	break
	ans += 1