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;

int n,m,dp[200009],ans;
vector<int>v[200002];

int dfs(int x){
  if(dp[x]!=-1) return dp[x];

  int res=0;
  for(int i=0;i<v[x].size();i++){
    res=max(res,dfs(v[x][i]) + 1 );
  }
  return dp[x] = res;
}


int main(){
  memset(dp,-1,sizeof(dp));
  cin>>n>>m;
  while(m--){
    int x,y;
    cin >> x >> y; x--; y--;
    v[x].push_back(y);
  }
  while(n--) ans = max(ans,dfs(n));

  cout<<ans<<endl;
}