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: Wrong Answer)

#include <bits/stdc++.h> 
using namespace std;
#define ll long long 
#define mod 1000000007
#define MOD 99824435300000000
inline ll mul(ll a,ll b){
  a=(a+MOD)%MOD;
  b=(b+MOD)%MOD;
  ll c=a*b;
  c=(c+MOD)%MOD;
  return c;
}
inline ll add(ll a,ll b){
  a=(a+MOD)%MOD;
  b=(b+MOD)%MOD;
  ll ans=(a+b);
  ans=(ans+MOD)%MOD;
  return ans;
}

ll power(ll a,ll b,ll c){
  ll ans=1;
  while(b){
    if(b&1){
      ans=mul(ans,a);
    }
    a=mul(a,a);
    b=b/2;
  }
  return ans;
}
inline ll max(ll a,ll b){return a>b?a:b;}
inline ll min(ll a,ll b){return a<b?a:b;}
void f(vector<int> v[],int dp[],int src,int vis[]){
  vis[src]=1;
  for(auto x: v[src]){
    if(!vis[x]){
      f(v,dp,x,vis);
      dp[src]=max(dp[src],1+dp[x]);
    }
    else dp[src]=max(dp[src],1+dp[x]);
  }
}
int main()
{
  int n,m; cin>>n>>m;
  vector<int> v[n+1];
  for(int i=0;i<m;++i){
    int a,b; cin>>a>>b;
    v[a].push_back(b);
  }
  int dp[n+1];
  memset(dp,0,sizeof(dp));
  int vis[n+1];
  memset(vis,0,sizeof(vis));
  for(int i=1;i<=n;++i){
    if(!vis[i])f(v,dp,1,vis);
  }
  int ans=0;
  for(int i=1;i<=n;++i)ans=max(ans,dp[i]);
  cout<<ans;
  return 0;
}