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;

vector<int> edges[100001];
int dp[100001] = {};
bool vis[100001] = {};

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

int main() {
	int N,M;
	cin >> N >> M;
	for(int i=0;i<M;i++) {
		int u, v;
		cin >> u >> v;
		edges[v].push_back(u);
	}
	int ans = 0;
	for(int i=1;i<=N;i++) {
		ans = max(ans, dfs(i));
	}
	cout << ans;
}