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;
int dp[100005];
vector<vector<int>> g;
int calc(int u)
{
    if(dp[u] != -1)
        return dp[u];

    dp[u] = 0;
    for (int i = 0; i < g[u].size(); ++i) {
        dp[u] = max(dp[u], calc(g[u][i])+1);
    }

    return dp[u];

}
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);

    memset(dp, -1, sizeof(dp));

    int n, m; cin >> n >> m;
    g.resize(n+1);
    for (int i = 0; i < m; ++i) {
        int x, y; cin >> x >> y;
        g[x].push_back(y);
    }
    for (int i = 1; i <= n; ++i) {
        g[0].push_back(i);
    }

    cout << calc(0) - 1 << endl;
    return 0;
}