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[100005];
int d[100005]={0},n,m,x,y;
void dfs(int no){
    for(int i=0;i<a[no].size();i++){
        if(!d[a[no][i]]) dfs(a[no][i]);
        d[no]=max(d[no],1+d[a[no][i]]);
    }
    return ;
}
int main(){
    cin>>n>>m;
    for(int i=0;i<m;i++){
        cin>>x>>y;
        a[x].push_back(y);
    }
    int ans=0;
    for(int i=1;i<=n;i++){
        if(!d[i]) dfs(i);
    }
    for(int i=1;i<=n;i++) ans=max(ans,d[i]);
    cout<<ans;
    return 0;
}