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<int>v[100001];
int dp[100001]={0};
bool vis[100001]={0};
int n,m;
vector<int>ans;
void dfs(int x){  
    if(vis[x])return ;
    vis[x]=1;
    for(int i=0;i<v[x].size();i++){
      if(!vis[v[x][i]])dfs(v[x][i]);
    dp[x]=max(dp[x],1+dp[v[x][i]]);
    }
}
int main(){
  cin>>n>>m;
  int x,y;
  for(int i=0;i<m;i++){
  cin>>x>>y;
    v[x].push_back(y);
  }
  for(int i=1;i<=n;i++){
  if(!vis[i])dfs(i);}
  cout<<*max_element(dp+1,dp+n+1);
}