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
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
'''
N, M = mi()
x = li2(M)

#dp = dp2(0, 2, N)
dp = [[0, []] for i1 in range(N+1)]


for i in range(M):
    dp[x[i][1]][0] = max(dp[x[i][1]][0], dp[x[i][0]][0] + 1)
    dp[x[i][0]][1].append(x[i][1])
    if dp[x[i][1]][1] != []:
        for a in dp[x[i][1]][1]:
            dp[a][0] = max(dp[x[i][1]][0] + 1, dp[a][0])

print(dp)
print(max([row[0] for row in dp])) 
'''
from collections import deque
N, M = mi()
x = li2(M)

h = [0]*N
adj = [[] for i in range(N)]
for i in range(M):
    x[i][0] -= 1
    x[i][1] -= 1
    h[x[i][1]] += 1
    adj[x[i][0]].append(x[i][1])

zeros = deque([])
ans = []
for i in range(N):
    if h[i] == 0:
        zeros.append(i)
        ans.append(i)

while(zeros != deque()):
    a = zeros.popleft()
    if(adj[a]):
        for b in adj[a]:
            h[b] -= 1
            if h[b] == 0:
                zeros.append(b)
                ans.append(b)

#print(ans)

dp = [0]*N
#print(ans)
#print(adj)
for a in ans:
    #print(dp)
    if adj[a]:
        for b in adj[a]:
            dp[b] = max(dp[a] + 1, dp[b])
#print(dp)
print(dp[ans[-1]])