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 dp[100005], cont = 0;
int f(int u, vector<vector<int>>&lad){
	if(dp[u]) return dp[u];
	dp[u] = 1;
	for(auto x: lad[u])
		dp[u] = max(dp[u], f(x, lad) + 1);
	
	return dp[u];
}
int main() {
	int n, m, u , v;
	cin >> n >> m;
	vector<vector<int>>lad(n);
	for(int i=0;i<m;i++){
		cin >> u >> v;
		u--, v--;
		lad[u].push_back(v);
	}
	memset(dp, 0 , sizeof(dp));
	int ans = f(0, lad);
	for(int i=1;i<n;i++)
		ans = max(ans,f(i, lad));
	cout << ans - 1;
	return 0;
}