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 pb push_back

int n,m,dist[100010],cor[100010],gr[100010];
vector<int> G[100010];
int ans=0;
void dfs(int v){
	cor[v]=1;
	int parc=0;
	for(auto &u:G[v]){
		if(!cor[u]){	
			dfs(u);
		}
		parc= max(dist[u],parc);
	}
	dist[v] = parc+1;
	ans = max(ans,dist[v]-1);
}

int32_t main(){
	cin >> n >> m;
	while(m--){
		int x,y;
		cin >> x >> y;
		gr[y]++;
		G[x].pb(y);
	}
	for(int i=1;i<=n;i++){
		if(!gr[i])
			dfs(i);
	}
	cout << ans << '\n';
}