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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
sys.setrecursionlimit(10**9)

def dfs(x): #グラフでの再帰DFS
    if dp[x] != -1:
        return dp[x] #すでに値が決まっていたらそれをかえす
    ans = 0
    for e in graph[x]: #すべての枝について
        ans = max(ans,1 + dfs(e))
    dp[x] = ans
    return ans # 最も長い距離を返す　

n,m = list(map(int, input().split()))

graph = [[] for i in range(n+1)]
dp = [-1]
for i in range(1,n+1):
    dp.append(-1) # dpは初期値-1

for _ in range(m): # グラフの作成
    a,b = map(int, input().split())
    graph[a].append(b)
    #graph[b].append(a) #無向グラフの時
    
ans=0

for i in range(1,n+1):
    ans=max(ans,dfs(i))
print(ans)