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>
#define N_ 101000
using namespace std;
int Deg[N_],Q[N_],head,tail,n,m,D[N_],res,a,b;
vector<int> E[N_];
int main()
{
	cin>>n>>m;
	for (int i=0;i<m;i++) cin>>a>>b,E[a].push_back(b),Deg[b]++;
	for (int i=1;i<=n;i++) if (!Deg[i]) Q[++tail]=i;
	while (head<tail)
	{
		int x=Q[++head];
		res=max(res,D[x]);
		for (auto &y : E[x])
		{
			Deg[y]--;
			D[y]=max(D[y], D[x] + 1);
			if (!Deg[y]) Q[++tail] = y;
		}
	}
	cout<<res;
	return 0;
}