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
#define rep(i,n) for(int i=0;i<n;i++)
int n,m,a,b,dp[111111],ans;
vector<int>v[111111];
int dfs(int x){
	if(dp[x])return dp[x];
	rep(i,v[x].size())dp[x]=max(dfs(v[x][i])+1,dp[x]);
	ans=max(ans,dp[x]);
	return dp[x];
}
signed main(){
	cin>>n>>m;
	rep(i,m){
		cin>>a>>b;
		a--,b--;
		v[a].push_back(b);
	}
	rep(i,n)if(!dp[i])dfs(i);
	cout<<ans<<endl;
	return 0;
}