Problem: 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.

Examples

Input

4 5
1 2
1 3
3 2
2 4
3 4


Output

3


Input

6 3
2 3
4 5
5 6


Output

2


Input

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3


Output

3

Solution (in PYTHON3):

Solution:
import sys
readline = sys.stdin.readline
sys.setrecursionlimit(10 ** 5 + 1)

N,M = map(int,readline().split())

G = [[] for i in range(N)]

for i in range(M):
  x,y = map(int,readline().split())
  G[x - 1].append(y - 1)

dp = [-1] * N

def rec(v):
  if dp[v] != -1:
    return dp[v] # 更新済み
  
  res = 0
  for child in G[v]:
    res = max(res, rec(child) + 1)
    
  dp[v] = res
  return res

res = 0
for v in range(N):
  res = max(res, rec(v))
  
print(res)