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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;

#define REP(i, n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i, m, n) for(int i = (int)(m); i < (int)(n); ++i)

int dfs(int pos, vector<vector<int>>& G, vector<int>& memo)
{
    if(memo[pos] > 0) return memo[pos];

    int ret = 0;
    for(auto v: G[pos]) ret = max(ret, dfs(v, G, memo)+1);
    return memo[pos] = ret;
}

int main()
{
    int N, M;
    cin >> N >> M;
    vector<vector<int>> G(N);
    REP(i, M){
        int x, y;
        cin >> x >> y;
        --x, --y;
        G[x].push_back(y);
    }

    int ans = 0;
    vector<int> memo(N, 0);
    REP(i, N) ans = max(ans, dfs(i, G, memo));
    cout << ans << endl;

    return 0;
}