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 fi first
#define se second
#define pb push_back
#define all(x) x.begin(), x.end()
typedef pair<int,int> pii;
typedef pair <long long,long long> pll;
typedef long long ll; 
typedef long double ld; 
const ll mod = 1e9+7;
int solve(int src, vector<int> &dp,vector <vector <int > > &g)
{
	if(dp[src] != -1)
		return dp[src];
	bool isLeaf = true;
	int maxVal = 0;
	for(int &x : g[src])
	{
		isLeaf = false;
		maxVal = max(maxVal, solve(x,dp,g));
	}	
	return dp[src] = isLeaf ? 0 : 1 + maxVal ;
}

int main(){
    ios_base::sync_with_stdio(false); cin.tie(NULL); 
    int n,m; cin >> n>> m;
    vector <vector <int > > g(100001);
    vector <int> dp(100001,-1);
    for(int i=0 ; i < m; i++)
    {	int u,v;
		cin >> u >> v;
		g[u].pb(v);
	}
	int ans = INT_MIN;
	for(int i = 1 ;i <=n ; i++)
		ans = max(ans, solve(i,dp,g));
		
	cout << ans;
    return 0;
}