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;
vector<int>graph[1000001];
int dp[1000001];
int solve(int src){
    if(dp[src] != -1){
        return dp[src];
    }
    bool leaf = 1;
    int bestchild = 0;
    for(auto child: graph[src]){
       leaf = 0;
       bestchild  =max(bestchild , solve(child));
    }
    if(leaf == 1){
        return dp[src] = 0;
    }else{
        return dp[src] = 1 + bestchild;
    }
}
int main(){
    memset(dp , -1 , sizeof(dp));
    int n , m;
    cin>>n>>m;
    for(int i=0 ; i<m ; i++){
        int x , y;
        cin>>x>>y;
        graph[x].push_back(y);
    }
    int ans = 0;
    for(int i=1 ; i<=n ; i++){
        ans = max(ans , solve(i));
    }
    cout<<ans;
    return 0;
}