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;
vector<vector<int> > v;
int dp[100001];
int dfs(int i)
{
    if(dp[i]!=1)return dp[i];
    else 
    {for(int j=0;j<v[i].size();j++)
    {
        dp[i]=max(dp[i],1+dfs(v[i][j]));
    }
       return dp[i]; 
    }
}
int main()
{
    int n,m;
    cin>>n>>m;
    v.resize(n+1);
    for(int i=0;i<=100001;i++)dp[i]=1;
for(int i=0;i<m;i++)
{
    int x,y;
    cin>>x>>y;
    v[x].push_back(y);
}
int ans=-1;
for(int i=0;i<n;i++)
{
    ans=max(ans,dfs(i+1));
}
cout<<ans-1;
}