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:
from collections import deque
N,M = list(map(int,input().split()))
inflows = [0]*(N+1)
edges = [[] for i in range(N+1)]
for i in range(M):
    x,y = list(map(int,input().split()))
    edges[x].append(y)
    inflows[y] += 1

queue = deque([i for i in range(1,N+1) if inflows[i] == 0])
DP = [0]*(N+1)
while queue:
    x = queue.popleft()
    for y in edges[x]:
        inflows[y] -= 1
        DP[y] = max(DP[y],DP[x]+1)
        if inflows[y] == 0:
            queue.append(y)

print(max(DP))