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>
#define maxn 120000
using namespace std;
map<int, int> mp;
vector<int> G[maxn];
int f(int u){
	if(mp.count(u)) return mp[u];
	mp[u] = 0;
	for(int v : G[u]) mp[u] = max(mp[u], f(v) + 1);
	return mp[u];
}
int main(){
	ios::sync_with_stdio(false);
	int N, M;
	cin >> N >> M;
	while(M --){
		int x, y;
		cin >> x >> y;
		G[x].push_back(y);
	}
	int ans = 0;
	for(int i = 1; i <= N; i += 1) ans = max(ans, f(i));
	cout << ans;
}