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;
#define pb push_back
#define fr(i,n) for(int i=0;i++<n;)
#define Fr(i,n) for(int i=0;i<n;i++)

int n,m,x,y,dp[100010]={};
vector<int> e[100010]={};

int M(int i){
  if(dp[i]!=0) return dp[i];
  int s=e[i].size(),k=1;
  Fr(j,s) k=max(k,1+M(e[i][j]));
  dp[i]=k;
  return k;
}

int main(){
  cin>>n>>m;
  fr(i,m){cin>>x>>y;e[x].pb(y);}
  int ans=0;
  fr(i,n) ans=max(ans,M(i));
  cout<<ans-1<<endl;
}