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"
#include "sstream"
#define EPS 1e-9
using namespace std;
const int N=1e5+1,OO=0x3f3f3f3f;
typedef long long ll;
int n,m; vector<int>vc[N]; int dp[N];
int solve(int u){
    if(vc[u].empty())
        return 0;
    int &ret=dp[u];
    if(~ret)
        return ret;
    for(auto i:vc[u])
        ret=max(ret,1+solve(i));
    return ret;
}
int main() {
   cin>>n>>m; int x,y;
   while(m--)
       cin>>x>>y,vc[x].push_back(y);
   memset(dp,-1, sizeof(dp));
   int ans=0;
   for(int i=1;i<=n;i++)
   ans=max(ans,solve(i));
   cout<<ans;
}