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 N = 1e5 + 5;
int n, m, vis[N], dp[N];
vector<int> g[N];

void dfs(int v){
	vis[v] = 1;
	for(int u : g[v]){
		if(!vis[u])dfs(u);
		dp[v] = max(dp[v], 1 + dp[u]);
	}
}

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0); cout.tie(0);

	cin>>n>>m;
	for(int i=0;i<m;++i){
		int u, v; cin>>u>>v;
		g[u].push_back(v);
	}

	int ans = 0;
	for(int i=1;i<=n;++i)if(!vis[i]){
		dfs(i);
		ans = max(ans, dp[i]);
	}

	cout<<ans<<"\n";
}