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: Runtime Error)

// #Sazaの1日1AC
#include<bits/stdc++.h>
using namespace std;
const long long mod=1000000000+7;
const long long INF=1e16;

//マクロ
//型エイリアス
using ll = long long;
using P=pair<long long,long long>;
using vl=vector<long long>;
using vvl=vector<vector<long long>>;
//ショートカット
#define rep(i,n) for(int i=0;i<n;i++)
#define rep2(i,k,n) for(int i=k;i<n;i++) //半開区間
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(),v.rend()
#define pb push_back
//入力
#define vin(v,N) for(long long i=0;i<N;i++) cin>>v.at(i)
#define lin(n) long long n;cin>>n
#define vlin(v,N) vector<long long>v(N);for(long long i=0;i<N;i++)cin>>v.at(i)

#define max(a,b) max((ll)a,(ll)b)
#define min(a,b) min((ll)a,(ll)b)

//関数
//最大公約数
long long gcd(long long m, long long n){
  long long a=max(m,n);
  long long b=min(m,n);
  long long r=a%b;
  while(r!=0){
    a=b; b=r; r=a%b;
  }
  return b;
}
// 最小公倍数
long long lcd(long long m, long long n){
  return m*n/gcd(m,n);
}
//xのn乗
long long power(long long x, long long N){
  long long ret=1;
  for(long long i=0;i<N;i++)   
    ret*=x;
  return ret;
}
//繰り返し二乗法
long long repeat_squaring(long long x, long long n){
  if(n==0) return 1;
  else if(n%2==0){
    long long t=repeat_squaring(x,n/2);
    return t*t%mod;
  }
  else
    return x*repeat_squaring(x,n-1);
}
//nCr
long long Comb (long long n, long long r);
//nCr (mod)
long long modC(long long n, long long r) {
    vector<long long> f(n+1),inv(n+1),invf(n+1);
    f[0]=f[1]=1;
    invf[0]=invf[1]=1;
    inv[1]=1;
    for (long long i=2;i<n+1;i++) {
        f[i]=(i*f[i-1])%mod;
        inv[i]=mod-((mod/i)*inv[mod%i])%mod;
        invf[i]=(inv[i]*invf[i-1])%mod;
    }
    long long cmb=f[n]*(invf[r]*invf[n-r]%mod)%mod;
    if (n>=r) return cmb;
    else return 0;
}
//素因数分解(mapで返す)
map<long long,long long> factor(long long p){
  ll p1=p;
  map<long long,long long>ret;
  for(long long i=2;i*i<=p1;i++){
     while(p%i==0){
      ret[i]++;
      p/=i;
    }
  }
  if(p!=1)
  ret[p]++;
  return ret;
}
//素数判定
bool is_prime(long long N){
  for(long long i=2;i*i<=N;i++){
    if(N%i==0)
      return false;
  }
  return true;
}
//最大値更新
void chmax(long long &a,long long b){
  a=max(a,b);
}
//最小値更新
void chmin(long long &a,long long b){
  a=min(a,b);
}

//構造体
//Union-Find木
struct UnionFind{
  //メンバ変数 
  vector<long long>par; //par[i]:=頂点iの親
  vector<long long>s; //s[i]:=頂点iが属する集合の個数(iが根のとき)
  
  //コンストラクタ
  UnionFind(long long N):par(N),s(N){
    for(long long i=0;i<N;i++){
      par[i]=i; //最初はすべてが根として初期化
      s[i]=1;
    }
  }
  
  //メンバ関数
  //root(i):=頂点iの根
  long long root(long long i){
    if(par[i]==i) return i;
    par[i]=root(par[i]); //経路圧縮
    return root(par[i]); //再帰
  }
  //size[i]:=iが属する集合の個数
  long long size(long long i){
    return s[root(i)];
  }
  //same(x,y) xとyが同じ根を持つか(同じ集合に含まれるか)
  bool same(long long x, long long y){
    return root(x)==root(y);
  }
  //unite(x,y) xの根をyの根を繋げる(集合を合併)
  void unite(long long x, long long y){
    if(!same(x,y)){
      long long rx=root(x);
      long long ry=root(y);
      par[rx]=par[ry];
      s[ry]=s[rx]+s[ry];
    }
  }
};

//メイン関数
int main(){
  //doubleの桁数
  cout<<fixed<<setprecision(10);
  
  lin(N);lin(M);
  vvl G(N,vl(N,INF));
  rep(i,M){
    lin(x);lin(y); x--; y--;
    G[x][y]=-1;
  }
  
  ll res=0;
  rep(k,N){
    rep(i,N){
      rep(j,N){
        chmin(G[i][j], G[i][k]+G[k][j]);
      }
    }
  }
  
  rep(i,N){
    rep(j,N){
      chmax(res,-1*G[i][j]);
      cout<<i<<" "<<j<<":"<<-1*G[i][j]<<endl;
    }
  }
  
  cout<<res;
}