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;
using LL=long long;
vector<int>from[100001];
vector<int>dp;
int df(int i){
  if(dp[i]!=-1)
    return dp[i];
  dp[i]=0;
  for(int f:from[i])
    dp[i]=max(dp[i],df(f)+1);
  return dp[i];
}
int main(){
  int N,M;cin>>N>>M;
  for(int i=0;i<M;i++){
    int x,y;cin>>x>>y;
    from[y].push_back(x);
  }
  dp.resize(N+1,-1);
  for(int i=1;i<=N;i++)
    if(dp[i]==-1)df(i);
  cout<<*max_element(dp.begin(),dp.end())<<endl;
}