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: Time Limit Exceeded)

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

list<int> *adjList;

void dfs(int v,vector<int> &dis,int count)
{
    for(auto i=adjList[v].begin();i!=adjList[v].end();i++)
        dfs(*i,dis,count+1);
    if(dis[v]<count)
        dis[v]=count;
}

int main()
{
    int V,E;
    cin>>V>>E;
    adjList=new list<int>[V+1];
    int u,v;
    for(int i=0;i<E;i++)
    {
        cin>>u>>v;
        adjList[u].push_back(v);
    }
    vector<int> dis(V+1,0);
    for(int i=1;i<=V;i++)
    {
        dfs(i,dis,0);
    }
    int Max=INT_MIN;
    for(int i=1;i<=V;i++){
        Max=max(Max,dis[i]);
    }
    cout<<Max;
    return 0;
}