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 <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cmath>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
using namespace std;
typedef long long ll;
typedef vector<int> VI;
typedef vector<ll> VL;
typedef vector<string> VS;
typedef vector< vector<int> > VVI;
typedef vector< vector<ll> > VVL;
typedef pair<int,int> PII;
#define rep(i,n) for(int i=0;i<(n);i++)
#define all(a) (a).begin(),(a).end()
#define pf push_front
#define pb push_back
#define mp make_pair
#define ub upper_bound
#define lb lower_bound

int N,M;
VVI Z(100100);
VI ans(100100,-1);

void solve(int A){
  if(ans[A]!=-1) return;
  if(Z[A].size()){
    rep(i,Z[A].size()){
      solve(Z[A][i]);
      if(ans[A]==-1) ans[A]=ans[Z[A][i]]+1;
      else ans[A]=max(ans[A],ans[Z[A][i]]+1);
    }
  }else ans[A]=0;
}

int main(){
  cin>>N>>M;
  VI X(M),Y(M);
  rep(i,M) cin>>X[i]>>Y[i];
  rep(i,M) Z[X[i]-1].pb(Y[i]-1);
  rep(i,N) solve(i);
  int tmp=0;
  rep(i,N) tmp=max(tmp,ans[i]);
  cout<<tmp<<endl;
}