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;

const int N = 1e5 + 5;
vector<int> adj[N];
bool vis[N];
int dp[N], ans;

void dfs(int u){
	vis[u] = true;
	for(auto v : adj[u]){
		if(!vis[v])
			dfs(v);
		dp[u] = max(dp[u], dp[v] + 1);
	}
}

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

	int x, y;
	for(int i = 1; i <= m; i++){
		cin >> x >> y;
		adj[x].emplace_back(y);
	}

	for(int i = 1; i <= n; i++)
		if(!vis[i])
			dfs(i);

	for(int i = 1; i <= n; i++)
		ans = max(ans, dp[i]);

	cout << ans << "\n";
}