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<int> a[200005];
int d[200005];
bool vis[200005]={false};
int go(int x){
    if(vis[x]!=0)
        return d[x];
    vis[x]=1;
    for(int i=0;i<a[x].size();i++){
        d[x]=max(d[x],go(a[x][i])+1);
    }
    return d[x];
}
int main()
{
    int x,y,i,j,k,n,m;
    cin>>n>>m;
    for(i=0;i<m;i++){
        cin>>x>>y;
        a[x].push_back(y);
    }
    int ans=0;
    for(i=1;i<=n;i++){
        if(!vis[i])
            ans=max(ans,go(i));
    }
    cout<<ans;
}