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
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 1e5+10;
vector<int>G[maxn];
ll f[maxn];
ll dfs(int u){
	if(f[u])return f[u];
	f[u] = 1;
	for(int v:G[u])f[u] = max(f[u],dfs(v)+1);
	return f[u];
}
int main(){
	int n,m;
	cin >> n >> m;
	for(int i = 1;i <= m;i++){
		int f,t;
		cin >> f >> t;
		G[f].push_back(t);
	}
	for(int i = 1;i <= n;i++)dfs(i);
	ll ans = -1;
	for(int i = 1;i <= n;i++)ans = max(ans,f[i]);
	cout << ans-1;
	return 0;
}