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;

vector<vector<int>> adj;
vector<int> memo;

int dfs(int x)
{
	if (memo[x] != -1)
		return memo[x];
		
	memo[x] = 0;
	for (int a : adj[x])
		memo[x] = max(memo[x], dfs(a) + 1);
	return memo[x];
}

int main()
{
	int N, M;
	cin >> N >> M;
	adj.resize(N);
	memo.resize(N, -1);
	for (int i = 0; i < M; ++i)
	{
		int x, y;
		cin >> x >> y;
		adj[--x].push_back(--y);
	}
	
	int ans = 0;
	for (int i = 0; i < N; ++i)
		ans = max(ans, dfs(i));
	cout << ans << '\n';
}