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;
typedef long long ll;
vector<vector<int> > v;
ll INF = 1e17;
ll n , m;
ll dp[100000 + 10];
ll dfs(ll  i){
    if(v[i].size() == 0)return 0 ;
    if(dp[i] != -1)return dp[i] ;
    ll ans = -INF;
    for(int j=0;j<v[i].size();j++){
        ans = max(ans , 1+dfs(v[i][j]));
    }
    return dp[i] = ans;
}
int main(){
  //  cout<<(sizeof dp)<<endl;
    cin>>n>>m;
    memset(dp,-1,sizeof dp);
    v.resize(n+2);
    for(int i=0;i<m;i++){
        int  l , r;
        cin>>l>>r;
        l--;r--;
        v[l].push_back(r);
    }
    ll ans1 = -INF;
    for(int i=0;i<n;i++){
        ans1 = max(ans1,dfs(i));
    }
    cout<<ans1<<endl;
    return 0;
}