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 <bits/stdc++.h>
using namespace std;

// メモ化再帰
int dp[100100];
int n, m;

int rec(int v, vector<vector<int>>&G){
    if (dp[v] != -1) return dp[v];
    int result = 0;
    
    for (auto nv : G[v]){
        result = max(result, rec(nv, G) + 1);
    }
    
    return dp[v] = result;
}

int main(){
    
    int n, m;
    cin >> n >> m;
    
    vector<vector<int>> G(n, vector<int>());
    
    // 有向グラフの入力
    
    for (int i = 0; i < m; i++){
        int x, y;
        cin >> x >> y;
        x--, y--;
        
        G[x].push_back(y);
    }
    
    // initialization
    for (int v = 0; v < n; v++) dp[v] = -1;
    
    
    //  DP の更新順序が非自明
    // 各点を調べる
    int ans = 0;
    for (int i = 0; i < n; i++) ans = max(ans, rec(i, G));
    cout << ans << endl;
}