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 <iostream>
#include <vector>

using namespace std;
const int N = 1e5+1;

vector < int > g[N];
int dp[N];

int dfs(int v) {
	if(dp[v]) return dp[v];
	if(g[v].size() == 0) return 0;
	for(int u : g[v]) {
		dp[v] = max(dp[v], dfs(u) + 1);
	}

	return dp[v];
}

int main() {
	int n, m;
	cin >> n >> m;
	for(int i = 0; i < m; i++) {
	  int a, b; cin >> a >> b;
		g[a].push_back(b);
	}

	int ans = 0;
	for(int i = 1; i <= n; i++) {
		if(dp[i] == 0) {
			dfs(i);
			ans = max(ans, dp[i]);
		}
	}

	cout << ans << endl;
}