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;
int dp[100005];
vector <vector <int> > V(100005);
int N,M,blank=-1;
int call(int i){
	if (V[i].empty())	return 0;
	if(dp[i]!=-1)		return dp[i];
	int ans = 0;
	for(auto x:V[i]){
		ans = max(ans,1+call(x));
	}
	return dp[i] = ans;
}

int main()
{
	cin>>N>>M;
	memset(dp,blank,sizeof(dp));
	int i,j,k,p,q,l;
	for(i=0;i<M;i++){
		cin>>p>>q;
		V[p].push_back(q);
	}
	for(i=1;i<=N;i++)
		V[0].push_back(i);
	cout<<call(0)-1;
	return 0;
}