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 N 200005
using namespace std;
vector<int> G[N];

int n, m, d[N], rt[N], cnt, f[N];
int tot = 0, fir[N], nxt[N << 1], to[N << 1];

inline void addEdge(int u, int v) {
    nxt[++tot] = fir[u], fir[u] = tot, to[tot] = v;
}

inline void topsort() {
    queue<int> q;
    while (!q.empty()) q.pop();
    for (int i = 1; i <= n; ++i)
        if (d[i] == 0) q.push(i);
    while (!q.empty()) {
        int u = q.front(); q.pop();
        rt[++cnt] = u;
        for (int i = fir[u], v; i; i = nxt[i]) {
            v = to[i], d[v]--;
            if (d[v] == 0)
                q.push(v);
        }
    }
}

int main() {
#ifdef whyqx
    freopen("work.in", "r", stdin);
    freopen("work.out", "w", stdout);
#endif
    cin >> n >> m;
    for (int i = 1, u, v; i <= m; ++i)
        scanf("%d%d", &u, &v),
        addEdge(u, v), d[v]++, G[v].push_back(u);
    topsort();
    for (int k = 1; k <= cnt; ++k) {
        int u = rt[k];
        for (int i = 0, v, sz = G[u].size(); i < sz; ++i) {
            v = G[u][i];
            f[u] = max(f[u], f[v] + 1);
        }
    }
    int ans = 0;
    for (int i = 1; i <= n; ++i)
        ans = max(ans, f[i]);
    cout << ans << endl;
    return 0;
}