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;
const int MAX_nodes=1e5;
vector<int> adj[MAX_nodes+1];
vector<bool> visited(MAX_nodes+1, 0);
vector<int> cnt(MAX_nodes+1, 0);
void dfs(int u){
	visited[u]=true;
	for(auto v: adj[u]){
		if(!visited[v]) dfs(v);
		cnt[u]=max(cnt[u], cnt[v]+1);
	}
}
int main(){
	int n, m;
	cin >> n >> m;
	while(m--){
		int u, v;
		cin >> u >> v;
		adj[u].push_back(v);
	}
	int res=1;
	for(int i=1; i<=n; i++){
		if(!visited[i]) dfs(i);
		res=max(res, cnt[i]);
	}
	cout << res;
}