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 debug(x) cout << #x << "::" << x << endl;
#define debug2(x, y) cout << #x << "::" << x << " " << #y << "::" << y << endl;
#define debug3(x, y, z) cout << #x << "::" << x << " " << #y << "::" << y <<" "<< #z << "::" << z << endl;

#define For(i, a, b) for (int i = a; i < b; i++)

typedef long long ll;
const ll mod = 1e9 + 7;
const int MAX = 1e5 + 5;
typedef pair<int, int> pii;

void add(ll &a, ll b)
{
    a = (a + b) % mod;
    if (a < 0) a += mod;
}
vector<int> g[MAX];
vector<int> visit(MAX,-1);

int dfs(int num) {

   if(visit[num]!=-1) return visit[num];

   if(!g[num].size()) return 0;

    int ans = 0;
   for(auto child : g[num]) {
       ans = max(ans,dfs(child)+1);
   }

   visit[num] = ans;
   return ans;

}
int main() {

    int n,c;
    cin>>n>>c;

    For(i,0,c){
        int x,y;
        cin>>x>>y;
        g[x].push_back(y);
    }

    int ans = 0;

    For(i,1,n+1){
        ans = max(ans,dfs(i));
    }

    cout<<ans<<endl;

    return 0;

}