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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;

#define ff              first
#define ss              second
#define int             long long
#define pb              push_back
#define mp              make_pair
#define pii             pair<int,int>
#define vi              vector<int>
#define mii             map<int,int>
#define pqb             priority_queue<int>
#define pqs             priority_queue<int,vi,greater<int> >
#define setbits(x)      __builtin_popcountll(x)
#define zrobits(x)      __builtin_ctzll(x)
#define mod             1000000007
#define inf             1e18
#define ps(x,y)         fixed<<setprecision(y)<<x
mt19937                 rng(chrono::steady_clock::now().time_since_epoch().count());

const int MAXN = 1e5+5;
vector <int> adj[MAXN];
int maxD = INT_MIN,maxNode = -1;
int cache[MAXN];
void c_p_c()
{
  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#ifndef ONLINE_JUDGE
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif
}
int dfs(int s)
{
	if(cache[s] != -1)
	{
		return cache[s];
	}
	bool leaf = true;
	int ans = INT_MIN;
	for(int u:adj[s])
	{
		leaf = false;
		ans = max(ans,dfs(u));
	}
	if(leaf)
	{
		return 0;
	}
	else
	{
		return 1 + ans;
	}
}
int32_t main()
{
  c_p_c();
  memset(cache,-1,sizeof(cache));
  int n,m;
  cin >> n >> m;
  for(int i=0;i<m;i++)
  {
  	int x,y;
  	cin >> x >> y;
  	adj[x].push_back(y);
  }
  int res = INT_MIN;
  for(int i=1;i<=n;i++)
  {
  	res = max(res,dfs(i));
  }
  cout<<res<<endl;
  return 0;
}