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 n, m;
vector <int> v[100010];
int dp[100010];

void bust_dfs(int v1)
{
	int res = 0;
	for(auto j: v[v1])
	{
		if(dp[j] == 0) bust_dfs(j);
		res = max(res, dp[j] + 1);
	}
	dp[v1] = res;
}


int main()
{
	cin >> n >> m;
	for(int i = 1; i <= m; i++)
	{
		int h1, h2;
		cin >> h1 >> h2;
		v[h1].push_back(h2);
	}
	
	for(int i = 1; i <= n; i++)
	{
		bust_dfs(i);
	}
	sort(dp, dp + n + 1);
	cout << dp[n];
	return 0;
}