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 rep(i,a,n) for(ll i=a;i<n;i++)
#define ALL(s) s.begin(),s.end()
#define P pair<ll,ll>
#define vl vector<ll>
#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vvl vector<vector<ll>>
#define print(n) cout<<n<<endl
const int M=100111;
const int inf=1000000007;
const long long INF=1000000000000000007;
using ll=long long;
int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

int main(){
	ll n,m,x,y,dp[100010]={};
	cin>>n>>m;
	rep(i,0,m){
		cin>>x>>y;
		dp[y]=max(dp[x]+1,dp[y]);
	}
	ll ans=0;
	rep(i,1,n+1)ans=max(ans,dp[i]);
	print(ans);
}