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;
#define int long long

const int N=2e5+1, M=1e5+1;
int dp[N];
vector<int>adj[N];
bool visited[N];
int maxm=0, n, m;
void dfs(int x)
{
	if(visited[x])
		return;
	visited[x]=1;
	for(auto y:adj[x])
	{
		dfs(y);
		dp[x]=max(dp[x], dp[y]+1);
	}
	maxm=max(maxm, dp[x]);
}

int32_t main()
{
	cin>>n>>m;
	for (int i = 0; i < m; ++i)
	{
		int u, v;
		cin>>u>>v;
		adj[u].push_back(v);
	}
	for(int i=1; i<=n; ++i)
	{
		dfs(i);
	}
	cout<<maxm;
}