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

def dp(i, xy, l):
    if l[i] >= 0:
        return l[i]
    l[i] = t = max(dp(j, xy, l) for j in xy[i]) + 1
    return t

def main():
    sys.setrecursionlimit(10 ** 6)
    N, M = map(int, input().split())
    xy = [set() for _ in range(N)]
    for _ in range(M):
        xi, yi = map(int, input().split())
        xy[xi - 1].add(yi - 1)
    l = [0 if not i else -1 for i in xy]
    m = 0
    for i in range(N):
        m = max(m, dp(i, xy, l))
    print(m)


main()