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 <cstdio>
#include <algorithm>
#include <vector>

using namespace std;


const int MAX_N = 100005;

int n,m,dp[MAX_N];
vector<int> adjl[MAX_N];

int f(int i)
{
	if (dp[i]!=-1)
		return dp[i];
	int r=0;
	for (int x : adjl[i])
		r=max(r,1+f(x));
	return dp[i]=r;
}

int main()
{
	scanf("%d %d",&n,&m);
	for (int i=1; i<=n; i++)
		dp[i]=-1;
	while (m--)
	{
		int a,b;
		scanf("%d %d",&a,&b);
		adjl[a].push_back(b);
	}
	int ans=0;
	for (int i=1; i<=n; i++)
		ans=max(ans,f(i));
	printf("%d\n",ans);
	return 0;
}