Problem: 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.

Examples

Input

4 5
1 2
1 3
3 2
2 4
3 4


Output

3


Input

6 3
2 3
4 5
5 6


Output

2


Input

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3


Output

3

Solution (in CPP):

Solution:
#include <bits/stdc++.h> 
using namespace std;
const int N = 1e5+5;
vector<int> dp(N), n[N]; 
 
int lp(int i) {
  if(dp[i]) 
    return dp[i];
  for(auto p:n[i])
    dp[i]=max(dp[i], lp(p) + 1);
  return dp[i];
} 
int main() { 
  int N, M, x, y;
  cin >> N >> M; 
  for(int i = 0; i < M; i++) 
    cin >> x >> y, n[x].push_back(y); 
  int rez = 0; 
  for(int i = 1; i <= N; i++) 
    rez  = max(rez, lp(i)); 
  cout << rez; 
  return 0; 
}