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: Time Limit Exceeded)

#include<bits/stdc++.h>
 
#define rep(i,n) for(ll i = 0;i < n;++i)
#define all(v) v.begin(),v.end()
using namespace std;
using ll = long long;
typedef pair<int,int> P;
 
const int INF = 1001001001;
const long double PI = (acos(-1));
const int mod = 1e9+7;
const int vx[4] = {0,1,0,-1};
const int vy[4] = {1,0,-1,0};

vector<int> dp;
int mx = 0;
int f(vector<vector<int>> g,int n){
    if(dp[n] != -1) return dp[n];
    for(int a : g[n]){
        dp[n] = max(dp[n],f(g,a)+1);
    }
    return max(dp[n],0);
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n,m;
    cin >> n >> m;
    vector<vector<int>> g(n,vector<int> (0));
    rep(i,m){
        int x,y;
        cin >> x >> y;
        x--;y--;
        g[x].push_back(y);
    }
    dp = vector<int> (n,-1);
    rep(i,n){
        f(g,i);
    }
    
    int ans = 0;
    rep(i,n) {  
        ans = max(ans,dp[i]);
    }
    cout << ans << endl;


    cout << endl;
    return 0;
}