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**9)

def f(x):#dpは
    if dp[x]!=-1:
        return dp[x]#すでに値が決まっていたらそれをかえす
    ans=0
    for e in d[x]:#すべての枝について
        ans=max(ans,1+f(e))
    dp[x]=ans
    return ans

n,m = list(map(int, input().split()))

d={}
dp=[-1]
for i in range(1,n+1):
    d[i]=[]#dは初期値を[]
    dp.append(-1)#dpは初期値-1

for _ in range(m):
    a,b = map(int, input().split())
    d[a].append(b)#有向グラフをdictで
    
ans=0
for i in range(1,n+1):
    ans=max(ans,f(i))
print(ans)