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 100005
using namespace std;
int d[N],n,m,x,y,q[N],f,r,has[N],ans;
vector<int> v[N];
int main()
{
	scanf("%d%d",&n,&m);
	while(m--)
	{
		scanf("%d%d",&x,&y);
		x--;y--;
		v[x].push_back(y);
		has[y]++;
	}
	for(int i=0;i<n;i++)
	if(!has[i])
	q[r++]=i;
	while(f<r)
	{
		x=q[f++];
		for(int i=0;i<v[x].size();i++)
		{
			y=v[x][i];
			if(d[x]+1>d[y])d[y]=d[x]+1;
			if(ans<d[y])ans=d[y];
			has[y]--;
			if(!has[y])q[r++]=y;
		}
	}
	printf("%d\n",ans);
	return 0;
}