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;
typedef long long int ll;
ll n,m;
vector <ll> arr[100005];
ll dp[100005];

ll solve(ll i){
	
	if(dp[i]==-1){
		ll z = 0;
		for(ll j=0;j<arr[i].size();++j){
			
			z = max(z,solve(arr[i][j]));
			
		}
		dp[i] = 1+z;
		
	}
	return dp[i];
	
}

int main(){
	memset(dp,-1,sizeof(dp));
	cin>>n>>m;
	for(ll i=0;i<m;i++){
		
		ll x,y;
		cin>>x>>y;
		arr[x-1].push_back(y-1);
	}
	m = 0;
	for(ll i=0;i<n;i++){
		
		m = max(m,solve(i));
		
	}
	cout<<m-1<<endl;
	
}