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:
N,M=[int(x) for x in raw_input().split()]
A=[[] for i in range(N)]
B=[[] for i in range(N)]
C=[-1 for i in range(N)]
D=[0 for i in range(N)]
E=[0 for i in range(N)]

for i in range(M):
    a,b=[int(x)-1 for x in raw_input().split()]
    A[a].append(b) #to
    B[b].append(a) #from
F=[]
s=0
for i in range(N):
    D[i]=len(B[i])
    if D[i]==0:
        F.append(i)
        C[i]=0
        for a in A[i]:
            E[a]+=1
        s+=1
level=0
while s<N:
    level+=1
    Fnew=[]
    T=[]
    for f in F:
        for a in A[f]:
            if E[a]==D[a]:
                C[a]=level
                Fnew.append(a)
                s+=1
                E[a]=0
                for aa in A[a]:
                    T.append(aa)
    F=Fnew[:]
    for aa in T:
        E[aa]+=1
print max(C)