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:
from sys import stdin, exit, setrecursionlimit
setrecursionlimit(100000000)

input = stdin.readline
lmi = lambda: list(map(int, input().split()))
mi = lambda: map(int, input().split())
si = lambda: input().strip('\n')
ssi = lambda: input().strip('\n').split()


def dfs(node):
    if len(graph[node]) == 0:
        dp[node] = 0
        return 0
    if dp[node] != -1: return dp[node]
    ans = 0
    for i in graph[node]:
        ans = max(ans, dfs(i)+1)
    dp[node] = ans
    return ans


n, m = mi()
graph= [[] for i in range(n+1)]
for i in range(m):
    a, b = mi()
    graph[a].append(b)
dp = [-1]*(n+1)
for i in range(1, n+1):
    if dp[i] == -1:
        dfs(i)
print(max(dp))