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;
const int MAXN=100000+5;
int n,m,dp[MAXN],x,y,deg[MAXN],ans;
vector<int> V[MAXN];

int main(){
	cin>>n>>m;
	for(int i=0;i<m;++i) cin>>x>>y,++deg[y],V[x].push_back(y);
	queue<int> Q;
	for(int i=1;i<=n;++i) if(!deg[i]) Q.push(i);
	while(Q.size()){
		int p=Q.front(); Q.pop();
		for(int i=0;i<V[p].size();++i){
			--deg[V[p][i]],dp[V[p][i]]=max(dp[V[p][i]],dp[p]+1),ans=max(ans,dp[V[p][i]]);
			if(!deg[V[p][i]]) Q.push(V[p][i]);
		}
	}
	cout<<ans<<'\n';
	return 0;
}