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 Python (3.4.3) (judge verdict: Runtime Error)

from _collections import defaultdict
import sys

class Graph:

    def __init__(self, n):
        self.g = defaultdict(list)
        self.dp = [-1 for i in range(n + 1)]


    def add_edge(self, x, y):
        self.g[x].append(y)

    def longest_path_util(self, node):

        # if node not in self.g:
        #     # print(node)
        #     return 0

        if self.dp[node] != -1:
            return self.dp[node]

        leaf = 1
        best_child = 0
        for neib in self.g[node]:
                leaf = 0
                best_child = max(best_child, self.longest_path_util(neib))

        if leaf != 0:

            self.dp[node] = 0

        else:
            self.dp[node] = best_child + 1

        return self.dp[node]


    def longest_path(self, n):

        for i in range(1, n + 1):

            if self.dp[i] == -1:
                self.longest_path_util(i)

        return max(self.dp)


n, k =  list(map(int, sys.stdin.readline().split()))
graph = Graph(n)
for _ in range(k):
    x, y = list(map(int, sys.stdin.readline().split()))
    graph.add_edge(x, y)

# print(graph.g)
print(graph.longest_path(n))