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;
#define FOR(i,a,b) for(int i=a;i<b;i++)
#define rep(i,b) FOR(i,0,b)
#define INF mugen
#define dump(x) cerr<<#x<<"="<<x<<endl
#define all(a) (a).begin(),(a).end()
typedef vector<int> vi;
typedef vector<vi> vii;
typedef vector<vii> viii;
typedef pair<int,int> P;
template <class T> void chmin(T & a, T const & b) { if (b < a) a = b; }
template <typename T>
string to_string(const T &n){ostringstream stm;stm << n;return stm.str();}
inline int toInt(string s) { int v; istringstream sin(s); sin >> v; return v; }
using ll = long long;
const ll mod = LLONG_MAX;

vector<int> G[112345];
int dp[100100];
int rec(int v){
    if(dp[v]!=-1)return dp[v];

    int res=0;
    for(auto nv:G[v]){
        res=max(res,rec(nv)+1);
    }
    dp[v]=res;
    return res;
}
signed main(){
    int N,M;
    cin>>N>>M;
    rep(i,M){
        int x,y;
        cin>>x>>y;
        x--;y--;
        G[x].push_back(y);
    }
    rep(i,N)dp[i]=-1;

    int res=0;
    rep(i,N)res=max(res,rec(i));
    cout<<res<<endl;


 
}