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>
using namespace std;
int dp[100010],l[100010],ans = 0;
vector<int> G[100010];
int dfs(int s){
	if(l[s]!=-1) return l[s];
	int mx = -1;
	for(int v:G[s]){
		mx = max(mx,dfs(v));
	}
	l[s] = mx + 1;
	return l[s];
}

int main(){
	int i,n,m;
	cin >> n >> m;
	for(i=0;i<m;i++){
		int a,b;
		cin >> a >> b;
		a--; b--;
		G[a].push_back(b);
	}
	for(i=0;i<n;i++) l[i] = -1;
	for(i=0;i<n;i++){
		if(l[i]==-1) dfs(i);
	}
	for(i=0;i<n;i++) ans = max(ans,l[i]);
	cout << ans << endl;
}