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;

vector<vector<int>> g;
int dp[100010];

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(){
  int n,m;
  cin>>n>>m;
  g.assign(n, vector<int>());

  for(int i=0; i<m; ++i){
    int x,y;
    cin>>x>>y;
    g[x-1].push_back(y-1);
  }

  for(int i=0; i<n; ++i)dp[i]=-1;

  int ans=0;
  for(int v=0; v<n; ++v)ans=max(ans, rec(v));

  cout<<ans<<endl;
}