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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL) ;
#define MOD 1000000007
#define int long long
#define pb push_back
#define pii pair<int,int>
#define vi vector<int>
#define vvi vector<vector<int>>
#define vpii vector<pair<int,int>>
#define ff first
#define ss second
#define INF (1LL<<61)

using namespace std;

int n, m;
vi adj[500010];
int vis[500010];
int dp[500010];

void dfs(int sv) {

	vis[sv] = 1;
	for (auto ch : adj[sv]) {
		if (!vis[ch])
			dfs(ch);

		dp[sv] = max(dp[sv] , 1 + dp[ch]);

	}

}



int32_t main() {

	fastio
// #ifndef ONLINE_JUDGE
// freopen("input.txt", "r", stdin);
// freopen("output.txt","w", stdout);
// #endif

	cin >> n >> m;
	for (int i = 1 ; i <= m ; i++) {
		int x , y;
		cin >> x >> y;
		adj[x].pb(y);
	}

	for (int i = 1 ; i <= n ; i++)if (!vis[i])dfs(i);

	int ans = 0;
	for (int i = 1 ; i <= n ; i++)ans = max(ans , dp[i]);
	cout << ans << '\n';

	return 0;
}