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
from functools import lru_cache
sys.setrecursionlimit(524287)

n,m,*l = map(int,open(0).read().split())
pas = [[] for _ in range(n)]
for x,y in zip(l[::2],l[1::2]):
	pas[x-1].append(y-1)

INF = float("inf")
done = [-INF]*n

@lru_cache(maxsize = None)
def dfs(t):
	if done[t] >= 0:
		pass
	elif pas[t]:
		done[t] = max(dfs(s) for s in pas[t]) + 1
	else:
		done[t] = 0
	return done[t]

print(max(dfs(i) for i in range(n)))