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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

const int nax = 1e5 + 5;
vector<int> edges[nax];
int in_degree[nax];
int dist[nax];
bool visited[nax];
void dfs(int a){
    visited[a] = true;
    for(int b:edges[a])
    {
        dist[b] = max(dist[b],dist[a]+1);
        --in_degree[b];
        if(in_degree[b] == 0)
        {
            dfs(b);
        }
    }
}

int main()
{
    int n,m;
    cin >> n >> m;
    
    while(m--)
    {
        int a,b;
        cin >> a >> b;
        edges[a].push_back(b);
        ++in_degree[b];
    }
    for(int i=1;i<=n;++i)
    {
        if(!visited[i] && in_degree[i]==0)
        dfs(i);
    }
    int answer = 0;
    for(int i=1;i<=n;++i)
    {
        answer = max(answer,dist[i]);
    }   
    cout << answer;
}