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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int N,M;
int x,y;
int D[100005];
vector<int> grafo[100005];

int F(int k){
	if(D[k])
		return D[k];
	D[k]=1;
	for(int f:grafo[k])
		D[k]=max(D[k],F(f)+1);
	return D[k];
}

int main(){

	cin>>N>>M;
	for(int i=0;i<M;i++){
		cin>>x>>y;
		x--,y--;
		grafo[x].push_back(y);
	}
	
	for(int i=0;i<N;i++)
		F(i);
	cout<<*max_element(D,D+N)-1;
}