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: Wrong Answer)

#include <bits/stdc++.h>

#define pb push_back

using namespace std;

const int N = 1e5 + 123;

int n, m;

int d1[N], d2[N], ans, used[N];

vector <int> g[N], q[N];

void dfs1 (int v, int p) {
    used[v] = true;
    for (auto to : q[v]) {
        if (!used[to]) {
            dfs1 (to, v);
            d2[v] = max (d2[v], d2[to] + 1);
        }
    }
}

void dfs2 (int v, int p) {
    used[v] = true;
    for (auto to : g[v]) {
        if (!used[to]) {
            dfs2 (to, v);
            d1[v] = max (d1[v], d1[to] + 1);
        }
    }ans = max (ans, d1[v] + d2[v]);
}

int main () {
    cin >> n >> m;
    for (int i = 1;i <= m;i ++) {
        int l, r;
        cin >> l >> r;
        g[l].pb (r);
        q[r].pb (l);
    }for (int i = 1;i <= n;i ++) {
        dfs1 (i, -1);
        dfs2 (i, -1);
    }
    cout << ans;
}