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;

int N, M, dp[100000], ans;
vector<int> G[100000];

int rec(int v){
	if(dp[v] != -1) return dp[v];
	int ma = -1;
	for(int i=0; i<G[v].size(); i++){
		if(ma < rec(G[v][i])) ma = rec(G[v][i]);
	}
	ma++;
	return dp[v] = ma;
}

int main(){
	cin >> N >> M;
	for(int i=0; i<M; i++){
		int x, y; cin >> x >> y;
		x--; y--;
		G[x].push_back(y);
	}
	fill(dp, dp+N, -1);
	for(int i=0; i<N; i++)
		if(ans < rec(i)) ans = rec(i);
	cout << ans << "\n";
	return 0;
}