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<cstdio>
#include<vector>
#include<algorithm>

using namespace std;

vector<int> ed[200000];

int dp[200000];
int dfs(int x)
{
  if(dp[x])return dp[x];
  dp[x]=0;for(int i=0;i<ed[x].size();i++)dp[x]=max(dp[x],dfs(ed[x][i])+1);
  return dp[x];
}

int main()
{
  int n=0,m=0;scanf("%d%d",&n,&m);for(int i=1,a=0,b=0;i<=m;i++){scanf("%d%d",&a,&b);ed[a].push_back(b);}
  for(int i=1;i<=n;i++)if(!dp[i])dfs(i);
  int maxn=0;for(int i=1;i<=n;i++)maxn=max(maxn,dp[i]);printf("%d",maxn);
  return 0;
}