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 MAXN = 1e5 + 10;

vector<int> grafo[MAXN];
int dp[MAXN],vis[MAXN],N,M;

int solve(int v){

	if(vis[v]) return dp[v];

	vis[v] = 1;
	int best = 0;

	for(int u : grafo[v]){
		best = max(best, solve(u) + 1 );
	}

	return dp[v] = best;

}

int main(){

	cin>>N>>M;
	for(int i = 1;i<=M;i++){
		int u,v;
		cin>>u>>v;
		grafo[u].push_back(v);
	}

	int best = 0;
	for(int i = 1;i<=N;i++) best = max(best, solve(i) );
	cout<<best<<endl;

	return 0;

}