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)

# coding:utf-8

import sys
from collections import defaultdict, deque

INF = 10 ** 5
MOD = 10 ** 9 + 7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return input()


n, m = LI()

G = defaultdict(list)
G2 = defaultdict
in_degree = [0] * n
for _ in range(m):
    x, y = LI_()
    G[x].append(y)
    in_degree[y] += 1

# トポロジカルソート
q = deque()
for v, e in enumerate(in_degree):
    if e == 0:
        q.append(v)

res = []
while q:
    v = q.popleft()
    res.append(v)
    for nv in G[v]:
        in_degree[nv] -= 1
        if in_degree[nv] == 0:
            q.append(nv)

dp = [0] * n
for v in res:
    for nv in G[v]:
        dp[nv] = max(dp[nv], dp[v] + 1)

print(max(dp))