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>
#define all(x) x.begin(), x.end()
using namespace std;

void dfs(int node, vector<vector<int>> & adj, vector<int> & dp){
    if(adj[node].size() == 0){
        dp[node] = 1;
        return;
    }

    if(dp[node] != 0)
        return;

    for(int x : adj[node]){
        dfs(x, adj, dp);
        dp[node] = max(dp[node], dp[x] + 1);
    }
}

int solve(vector<vector<int>> & adj, int n){
    vector<int> dp(n);

    for(int i = 0; i < n; i++)
        if(dp[i] == 0)
            dfs(i, adj, dp);

    return (*max_element(all(dp)))-1;
}

int main(){
    int n, m, x, y;
    cin>>n>>m;

    vector<vector<int>> adj(n);

    for(int i = 0; i < m; i++){
        cin>>x>>y;
        x--, y--;
        adj[x].push_back(y);
    }

    cout<<solve(adj, n);

    return 0;
}