Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in PyPy2 (5.6.0) (judge verdict: Runtime Error)

from collections import defaultdict, deque

n, m = [int(i) for i in raw_input().split()]

parents = defaultdict(list)

for _ in xrange(m):
    inp = raw_input().split()
    u = int(inp[0])
    v = int(inp[1])
    parents[v-1].append(u-1)

def get_f(parents, f, i):
    if f[i] != -1:
        return f[i]

    f[i] = 0
    for v in parents[i]:
        f[i] = max(f[i], get_f(parents, f, v) + 1)

    return f[i]

def longest_path(parents, n):
    f = [-1 for _ in xrange(n)]

    for i in xrange(n):
        get_f(parents, f, i)

    return max(f)

print longest_path(parents, n)