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[100001];
vector<int>G[100001];

int dfs(int u) {
	int &ret = dp[u];
	if(ret != -1)
		return ret;

	ret = 0;
	for(auto v : G[u])
		ret = max(ret, dfs(v)+1);

	return ret;
}

int main() {
	int u, v, V, E;
	cin >> V >> E;

	for(int i = 0; i < E; ++i) {
		cin >> u >> v;
		G[u].push_back(v);
	}

	memset(dp, -1, sizeof dp);
	int ans = 0;
	for(int i = 1; i <= V; ++i)
		ans = max(ans, dfs(i));

	cout << ans << endl;
	return 0;
}