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>> adj;
vector<int> dp;

int dfs(int v){
	if(dp[v]!=-1)
		return dp[v];
	dp[v]=1;
	for(auto c: adj[v]){
		dp[v]=max(dp[v],1+dfs(c));
	}
	return dp[v];
}
int main(){
	int n,m,res=0;
	cin >> n >> m;
	adj=vector<vector<int>>(n+1);
	dp=vector<int>(n+1,-1);
	for(int i=0;i<m;i++){
		int s,d;
		cin >> s >> d;
		adj[s].push_back(d);
	}
	for(int i=1;i<=n;i++){
		if(dp[i]==-1){
			res=max(res,dfs(i));
		}
	}
	if(res > 0)
		res-=1;
	cout<<res<<"\n";
}