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: Time Limit Exceeded)

#include<bits/stdc++.h>

using namespace std;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); ++i)
#define erep(i, n) for (ll i = 0; i <= (ll)(n); ++i)
#define FOR(i,a,b) for (ll i = (a); i < (ll)(b); ++i)
#define EFOR(i,a,b) for (ll i = (a); i <= (ll)(b); ++i)
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } }

vector<int> ans(10e5+5, -1);
using Graph = vector<vector<int>>;
int dfs(int node, Graph g) {
    //if(ans[node] != -1) return ans[node];

    ans[node] = 0;
    for(auto i : g[node]) {
        if(ans[i] != -1) chmax(ans[node], ans[i]+1);
        else chmax(ans[node], dfs(i, g) + 1);
    }
    return ans[node];
}

int main() {

    int n,m; cin >> n >> m;
    Graph g(n+1);
    for (int i = 0; i < m; ++i) {
        int from, to;
        cin >> from >> to;
        g[from].push_back(to);
    }

    int ret = 0;
    for(int i=1; i <= n; i++) {
        if(ans[i] != -1) chmax(ret, ans[i]);
        else chmax(ret, dfs(i, g));
    }

    cout << ret << endl;

    return 0;
}