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:
// G - Longest Path
#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
using vvi = vector<vi>;
int in(){int x;cin>>x;return x;}

#define VMAX 100000
vvi V(VMAX);
vi D(VMAX,-1);

int dfs(int p){
	if(D[p]>-1 || V[p].size()<1) return D[p];
	int a=0; for(int c:V[p]) a = max(a, dfs(c)+1);
	return D[p] = a;
}

int main(){
	int N,M; cin>>N>>M;
	while(M--) V[in()-1].push_back(in()-1);
	int a = 0; while(N--) a = max(a, dfs(N)+1);
	cout<< a <<endl;
}