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 PYTHON):

Solution:
import decimal,math
from collections import Counter,defaultdict
from fractions import gcd
from bisect import bisect_right,bisect_left
decimal.getcontext().prec = 100
import sys
sys.setrecursionlimit(1000000)

adj=[]
n,m = map(int,raw_input().split())
for i in range(n+1):
	adj.append([])
dp=[0]*(n+1)	
def dd(l):
	if(dp[l]!=-1):
		return dp[l]
	ma=dd(adj[l][0])
	for j in range(1,len(adj[l])):
		ma=max(ma,dd(adj[l][j]))
	dp[l]=ma+1
	return ma+1	
for i in range(m):
	x,y = map(int,raw_input().split())
	adj[y].append(x)
	dp[y]=-1
ans=[]
for i in range(1,n+1):
	ans.append(dd(i))
	# print i
print max(ans)