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>
#include <unordered_set>

using namespace std;

int dp[100001];

vector<vector<int>> adj;

void dfs(int v, int u) 
{
	if (dp[v]) return;
	for (const auto& el : adj[v])
	{
		dfs(el, v);
		dp[v] = max(dp[v], dp[el] + 1);
	}
}


int main()
{
	int n, m; cin >> n >> m;

	adj.resize(n+1);
	while (m--)
	{
		int x, y; cin >> x >> y;
		adj[x].push_back(y);
	}

	for (auto i = 1; i <= n; i++)
		dfs(i, 0);

	cout << *max_element(begin(dp), end(dp)) << endl;
}