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:
n, m = map(int, input().split())
dp=[0]*(n+1)
e=[ set() for _ in range(n+1)]
for _ in range(m):
    a, b = map(int, input().split())
    e[a].add(b)
    dp[b]+=1

q=[0]*(n+1)
j=0
for z in range(len(dp)):
    if dp[z]==0:
        q[j]=z
        j=j+1
color=0
i=1
while i<j:
    end=j
    for qel in range(i, end):
        for w in e[q[qel]]:
            dp[w]-=1
            if dp[w]==0: 
                q[j]=w
                j=j+1
    i=end
    color=color+1

print(color-1)