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;
int n,m;

const int size=1e5+10;
vector<int> g[size];
int dp[size];

int path(int i){

  if(dp[i]) return dp[i];

  for(int &j:g[i]){
    dp[i]=max(dp[i],path(j)+1);
  }
  return dp[i];
}

int main(){

  scanf("%d %d",&n,&m);
  int x,y;

  for(int i=0;i<m;i++){
    scanf("%d %d",&x,&y);
    g[x].push_back(y);
  }
  
  int maxi=0;
  for(int i=1;i<=n;i++)
    maxi=max(maxi,path(i));

  printf("%d\n",maxi);

  return 0;
}