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;
vector<int> adj[100010];
int dp[100005];
int n,m;

int lp(int n)
{
    int &ret = dp[n];
    if(ret!=-1)
        return ret;

    ret = 0;

    for(int i=0;i<adj[n].size();i++)
    {
        ret = max(ret,lp(adj[n][i])+1);
    }
    return ret;
}
int main()
{
    cin>>n>>m;

    for(int i=0;i<m;i++)
    {
        int u,v;
        cin>>u>>v;
        adj[u].push_back(v);

    }

    memset(dp,-1,sizeof dp);
    int mx =-1;

    for(int i=1;i<=n;i++)
    {
        mx = max(mx,lp(i));
    }

    cout<<mx<<endl;
}