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 pb push_back
using namespace std;
const int DN=1e5+5;
int n,m,f,g,b[DN],a[DN],ma,dp[DN];
vector<int>v[DN];
void dfs(int nod)
{
	for(auto i:v[nod])
	{
		dp[i]=max(dp[i],dp[nod]+1);
		a[i]++;
		if(a[i]==b[i])
			dfs(i);
	}
}
int main()
{
    cin>>n>>m;
    while(m--)
    {
    	cin>>f>>g;
    	v[f].pb(g);
    	b[g]++;
    }
    for(int i=1;i<=n;i++)
    	if(b[i]==0)
    		dfs(i);
    for(int i=1;i<=n;i++)
    	ma=max(ma,dp[i]);
    cout<<ma;
}