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 <set>
#include <map>
#include <vector>
#include <algorithm>
#include <iomanip>
#include <climits>
#include <numeric>
#include <cmath>
#include <queue>
#include <sstream>
#include <string.h>
#include <bitset>

using namespace std;
typedef long long ll;

const ll INF = 1LL<<62;
int dp[100100];
int N, M;
vector<vector<int>> G;

int rec(int v) {
  if (dp[v] != -1) {
    return dp[v];
  }
  int res = 0;
  for (int nv : G[v]) {
    res = max(res, rec(nv) + 1);
  }
  return dp[v] = res;
}

int main() {
  cin >> N >> M;
  G.assign(N, vector<int>());
  for (int i = 0; i < M; i++) {
    int x, y;
    cin >> x >> y;
    x--; y--;
    G[x].push_back(y);
  }
  
  for (int i = 0; i < N; i++) {
    dp[i] = -1;
  }
  
  int res = 0;
  for (int v = 0; v < N; ++v) {
    res = max(res, rec(v));
  }
  cout << res << endl;
  return 0;
}