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;
using ll = long long int;
ll max(ll a, ll b){
    return a > b? a: b;
}
int dfs(vector< vector<int> > &g, vector<int> &dp, int ind) {
    if(dp[ind] != -1)
        return dp[ind];
    int h = 0;
    for(auto v: g[ind]) {
        h = max(h, dfs(g, dp, v));
    }
    dp[ind] = h+1;
    return dp[ind];
}
int main() {
    int n, m;
    cin >> n >> m;
    vector< vector<int> > g(n);
    for(int i = 0; i < m; i++) {
        int u, v;
        cin >> u >> v;
        g[u-1].push_back(v-1);
    }
    vector<int> dp(n, -1);
    dfs(g, dp, 0);
    int ans = 0;
    for(auto a: dp){
        ans = max(ans, a);
    }
    cout << ans << endl;
}