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;

int n,m,dp[100001],c;
vector<int>v[100001];

int fun(int i){
    if(v[i].empty())return 0;
    if(dp[i])return dp[i];
    for(int j=0;j<v[i].size();j++){
        dp[i]=max(dp[i],1+fun(v[i][j]));
    }
    return dp[i];
}

int main(){
cin>>n>>m;
int a,b;
for(int i=1;i<=m;i++){
    cin>>a>>b;
    v[a].push_back(b);
}
for(int i=1;i<=n;i++){
    c=max(c,fun(i));
}
cout<<c;
}