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 defaultdict
from functools import lru_cache
import sys
sys.setrecursionlimit(1000000)


N, M = map(int, input().split())
XY = [map(int, input().split()) for _ in range(M)]

dp = [-1 for _ in range(N + 1)]

x_to_y = defaultdict(list)
for x, y in XY:
    x_to_y[x].append(y)


@lru_cache(N)
def depth(n):
    ret = -1
    for y in x_to_y[n]:
        ret = max(ret, depth(y))
    return ret + 1


        
depths = [depth(n) for n in range(1, N + 1)]
print(max(depths))