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 itn int
vector<int> dp(100005,-1);
vector<int> e[100005];

int f(int g){
  if(dp[g]!=-1) return dp[g];
  int nx=0;
  for(int j=0;j<e[g].size();j++){
    nx=max(nx,f(e[g][j])+1);
  }
  dp[g]=nx;
  return nx;
}
signed main(){
  int a,b,c,d,n=0;
  cin>>a>>b;
  for(int i=0;i<b;i++){
    cin>>c>>d;
    e[c].push_back(d);
  }
  for(int i=1;i<=a;i++){
    n=max(n,f(i));
  }
  cout<<n<<"\n";
  return 0;
}