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 <stdio.h>
#include <vector>
using namespace std;
#define PB push_back
const int N=1e5+10;
int f[N];
vector<int> graph[N];
int max(int a,int b){return a>b?a:b;}
int dp(int n){
  if(f[n]>=0)return f[n];
  for(int i:graph[n])f[n]=max(f[n],dp(i)+1);
  return f[n]=max(f[n],0);
}
int main(){
  int n,m,l,r,ans=0;
  scanf("%d%d",&n,&m);
  for(int i=1;i<=n;i++)f[i]=-1;
  while(m--){
  	scanf("%d%d",&l,&r);
    graph[l].PB(r);
  }
  for(int i=1;i<=n;i++)ans=max(ans,dp(i));
  printf("%d\n",ans);
}