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 ll long long
const ll MAX = 1e5;
const ll inf = 1e15;
vector<vector<ll>> g(MAX+5);
ll in_degree[MAX+5];
bool vis[MAX+5];
ll dist[MAX+5];
void dfs( ll a ){
	assert( !vis[a] );
	vis[a] = true;
	for( auto b : g[a] ){
		dist[b] = max( dist[b], dist[a]+1LL );
		--in_degree[b];
		if( in_degree[b] == 0 )
			dfs( b );
	}
}
signed main(){
	ll n, m, i, j, x, y;
	cin >> n >> m;
	for( i = 1 ; i <= m ; i++ ){
		cin >> x >> y;
		g[x].push_back( y );
		++in_degree[y];
	}
	for( i = 1 ; i <= n; i++){
		if( !vis[i] && in_degree[i] == 0 ){
			dfs( i );
		}
	}
	ll ans = 0;
	for( i = 1 ; i <= n ; i++ )
		ans = max( ans, dist[i] );
	cout << ans << endl;
	return 0;
}