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 nmax=100005;
vector<vector<int>> g(nmax);
vector<int> d(nmax);
int f(int s){
  if(d[s]){
    return d[s];
  }
  int res=0;
  for(auto x:g[s]){
    res=max(res,f(x)+1);
  }
  return d[s]=res;
}
int main(){
  int n,m;cin >> n >> m;
  vector<int> h(n);
  for(int i=0;i<m;i++){
    int x,y;cin >> x >> y;
    x--,y--;
    g[x].push_back(y);
    h[y]++;
  }
  int ans=0;
  for(int i=0;i<n;i++){
    if(!h[i]){
      ans=max(ans,f(i));
    }
  }
  cout << ans << endl;
}