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 M=1e5+5;
vector<int> g[M];

int dp[M];
int dfs(int u)
{
	if(dp[u]) return dp[u];
	for(int v:g[u])
		dp[u]=max(dp[u],dfs(v));
	return ++dp[u];
}

int main()
{
	int n,m; scanf("%d%d",&n,&m);
	int u,v;
	for(int i=0;i<m;i++)
	{
		scanf("%d%d",&u,&v);
		g[u].push_back(v);
	}
	int ans=0;
	for(int i=1;i<=n;i++)
		ans=max(ans,dfs(i));
	printf("%d\n",ans-1);
	return 0;
}