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 <iostream>
#include <cmath>
#include <algorithm>
#include<cmath>
#include <vector>
typedef long long ll;
using namespace std;
int dp[100005] , vis[100005];
vector<int>graph[100005];
void dfs(int node)
{
    vis[node] = 1;
    for (auto child : graph[node])
    {
        if (!vis [child])
            dfs(child);
        dp[node] = max(dp[child] + 1, dp[node]);
    }
}
int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int n, e,ans=0,u,v;
    cin >> n >> e;
    while (e--)
    {
        cin >> u >> v;
        graph[u].push_back(v);
    }
    for (int i = 1; i <= n; i++)
    {
        if (!vis[i])
            dfs(i);
    }
    for (int i = 1; i <= n; i++)
        ans = max(dp[i], ans);
    cout << ans;
    return 0;
}