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 ll long long int
vector<ll> v1[100005];
ll a[100005],vis[100005],t;
ll dfs(ll i)
{
    vis[i]=1;
    for(auto k:v1[i])
    {
        if(vis[k]==0) { t=dfs(k); a[i]=max(a[i],t+1); }
        else a[i]=max(a[i],a[k]+1);
    }
    return a[i];
}
int main()
{
    ll N,M,i,x,y,ans=0;
    cin>>N>>M;
    for(i=0;i<M;i++)
    { cin>>x>>y; v1[x].push_back(y);  }
    for(i=1;i<=N;i++)
    {  ans=max(ans,dfs(i));  }
    cout<<ans<<endl;
    return 0;
}