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;
map<int,vector<int> >mp;
int dp[100009],vis[100009];

void dfs(int n){
  vis[n]=1;
  for(int i=0;i<mp[n].size();i++){
  	if(!vis[mp[n][i]])
  	  dfs(mp[n][i]);
  dp[n]=max(dp[n],1+dp[mp[n][i]]);
  }
}
int main (){
int n,m,x,y;
cin>>n>>m;

while(m--)
cin>>x>>y,mp[x].push_back(y);

for(int i=1;i<=n;i++)
if(!vis[i])dfs(i);

int maxx=0;
for(int i=1;i<=n;i++)
  maxx=max(maxx,dp[i]); 

cout<<maxx<<endl;

return 0;
}