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
sys.setrecursionlimit(10**6)

N,M = map(int,input().split())
p = [list(map(int,input().split())) for _ in range(M)]
dp = [-1]*N
ip = [[] for _ in range(N)]
for i in range(M):
  ip[p[i][1]-1].append(p[i][0]-1)

#閉路がないため同じ頂点は通らない
#i番目の頂点に到達するまでの最長手数をメモ化再帰で求める

def maxpath(i):
  if dp[i] != -1:
    return dp[i]
  a = 0
  for el in ip[i]:
    a = max(a,maxpath(el)+1)
  dp[i] = a
  return a
  
for i in range(N):
  maxpath(i)

print(max(dp))