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 const max_n = 1e5 + 5;
vector<int> gr[100005];
int visited[max_n];

int dfs(int x){
	int ans = 0;
	if(visited[x] != -1) return visited[x];
	for(auto i : gr[x]) {
		ans = max(ans, dfs(i)+1);
	}
	visited[x] = ans;
	return ans;
}

int main(){
	int n, m, u, v;
	cin>>n>>m;
	for(int x=0;x<m;x++){
		cin>>u>>v;
		gr[u].push_back(v);
	}
	for(int x=0;x<max_n;x++) visited[x] = -1;
	int ans =0;
	for(int x=1;x<=n;x++) ans = max(ans, dfs(x));
	cout<<ans;
	return 0;
}