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 ll long long
using namespace std;
const ll N=(ll)2e5+100;
vector<ll>vec[N];
ll dp[N];
ll dfs(ll v)
{
	if(dp[v]!=-1)
		return dp[v];
	ll c=0;
	for(ll i=0;i<vec[v].size();i++)
	{
		c=max(c,dfs(vec[v][i])+1);
	}
	dp[v]=c;
	return c;
}
int main()
{
	ll n,m;
	cin>>n>>m;
	ll x,y;
	for(ll i=0;i<n+2;i++)
	{
		dp[i]=-1;
	}
	for(ll i=0;i<m;i++)
	{
		cin>>x>>y;
		vec[x].push_back(y);
	}
	ll ans=0;
	for(ll i=1;i<=n;i++)
	{
			ans=max(ans,dfs(i));
	}
	cout<<ans<<endl;
}