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;
typedef long long ll;
#define MAX 5 * 10000 + 1
#define INF 10000000000

int n, m;
vector<vector<int>> g;
vector<int> dp(int(1e5 + 10), 1);
int longestPath(int x)
{
    if (dp[x] != 1)
        return dp[x];
    
    for (int s: g[x])
        dp[x] = max(1+longestPath(s), dp[x]);
    return dp[x];
}


int main()
{
    cin >> n >> m;
    g.assign(n, vector<int>());
    for (int i = 0; i < m; ++i)
    {
        int u, v;
        cin >> u >> v;
        u--, v--;
        g[u].push_back(v);
    }
    int ans = -3;
    for (int i = 0; i < n; ++i)
    {
        ans = max(longestPath(i) - 1, ans);
    }
    cout << ans << endl;
    
    return 0;
}