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;
using ll=long long;
ll mod=1e9+7;
vector<int> adj[100003];
vector<int> dp(100003,-1);
int solve(int i)
{
  if(dp[i]!=-1)
  return dp[i];
  if(adj[i].empty())
  return dp[i]=0;
  int best=0;
  for(int x: adj[i])
  best=max(best,solve(x)+1);
  return dp[i]=best;
}
int main()
{
  int n,m,x,y;
  cin>>n>>m;
  for(int i=0;i<m;i++)
  {
    cin>>x>>y;
    adj[x].push_back(y);
  }
  for(int i=1;i<=n;i++)
  solve(i);
  cout<<*max_element(dp.begin(),dp.end())<<endl;
  return 0;
}