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>
#include <iostream>
using namespace std;

int longestpath(vector<vector<int>>v,vector<int>&dp,int i,int n)
{
    
        if(dp[i]==-1)
        {
            int edges=0;
            for(int j=0;j<v[i].size();j++)
            {
                int temp=longestpath(v,dp,v[i][j],n)+1;
                if(temp>edges)
                    edges=temp;
            }
            dp[i]=edges;
            return edges;
        }
    return dp[i];
}
int main()
{
    int n,m;
    cin>>n>>m;
    vector<vector<int>>v(n,vector<int>());
    int x,y;
    for(int i=0;i<m;i++)
    {
        cin>>x>>y;
        v[x-1].push_back(y-1);
    }
    vector<int>dp(n,-1);
    int j=0;
    while(j<n)
    {
    	longestpath(v,dp,j,n);
        j++;
    }
    int maxx=0;
    for(int i=0;i<n;i++)
    {
        maxx=max(dp[i],maxx);
    }
   	cout<<maxx<<endl;
    
	return 0;
}