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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define N 100010
#define pb push_back
#define int long long
#define pi pair<int , int>
#define mp make_pair
vector<int> edges[N];
bool visited[N];
bool arr[N];
int dp[N];
int parent[N];
int find(int x){
 if(parent[x] == -1){
 return x;
 }
 return find(parent[x]);
}
int n ,m;
void dfs(int st , int par){
	visited[st] = true;
	int ans = 0;
  for(auto it:edges[st]){
      if(!visited[it]){
	    dfs(it , st);
	    ans = max(ans , dp[it] + 1);
	}
  }
   dp[st] = max(dp[st] , ans);
}
int32_t main(){
	cin>>n>>m;
	for(int i = 0 ; i < m;i++){
	   int x , y;
	   cin>>x>>y;
	   edges[--x].pb(--y);
	}
	memset(dp , 0 , sizeof(dp));
	memset(visited , false , sizeof(visited));
	for(int i = 0 ;i < n ;i++){
	   if(!visited[i]){
	     dfs(i , i);
	   }
	}
	int maxi = -1;
	for(int i =0; i < n; i++){
	    maxi = max(maxi , dp[i]);
	}
	cout<<maxi<<endl;
	
}