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>
using namespace std;

#define ll long long
#define INF 1e9
#define fi first
#define se second

typedef vector <int> vi;
typedef pair <int, int> ii;

vector <vi> adj;
vi dp;

int dfs(int n) {
    if (dp[n] != -1) return dp[n];

    for (int i : adj[n]) {
        dp[n] = max(dp[n], dfs(i));
    }
    return ++dp[n];
}

int main() {
    int n, e;
    cin >> n >> e;

    adj.assign(n, vi(0));
    for (int i = 0; i < e; i++) {
        int a, b;
        cin >> a >> b;
        adj[a-1].push_back(b-1);
    }

    dp.assign(n, -1);

    for (int i = 0; i < n; i++) {
        if (dp[i] == -1) dfs(i);
    }

    int res = 0;
    for (int i = 0; i < n; i++) res = max(res, dp[i]);

    for (int i = 0; i < n; i++) cout << dp[i] << " ";
    cout << endl;

    cout << res << endl;
}