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;
vector<int> edges[100005];
void dfs(vector<int>& dp, int k){
	for(int i=0; i<edges[k].size(); i++){
		if(dp[edges[k][i]] == -1)
			dfs(dp, edges[k][i]);
		dp[k] = max(dp[edges[k][i]] + 1, dp[k] );
	}
}
int main()
{
	int n, m;
	cin>>n>>m;
	for(int i=0; i<m; i++){
		int a, b;
		cin>>a>>b;
		edges[a].push_back(b);
	}
	int ans = 0;
	vector<int> dp(n+1, -1);
	for(int i=1; i<=n; i++)
		edges[0].push_back(i);
	dfs(dp, 0);
	cout<<dp[0];
}