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[100009];
vector < int > v[100009];
int dfs(int node){
	int &ret = dp[node];
	if(ret != -1) return ret;
	ret = 0;
	for(int i=0;i<v[node].size();i++){
		int u = v[node][i];
		ret = max(ret,dfs(u)+1);
	}
	return ret;
}
int main(){
	memset(dp,-1,sizeof(dp));
	cin>>n>>m;
	for(int i=0;i<m;i++){
		int a,b;
		cin>>a>>b;
		a--;b--;
		v[a].push_back(b);
	}
	int mx = 0;
	for(int i=0;i<n;i++){
		mx = max(mx,dfs(i));
	}
	cout<<mx<<endl;
}