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 mxN=1e5;
int n, m, dp[mxN], ui, vi, ans;
vector<int> adj[mxN];

int cdp(int u) {
	if(!dp[u]) {
		for(int v : adj[u])
			dp[u]=max(cdp(v), dp[u]);
		++dp[u];
	}
	return dp[u];
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	cin >> n >> m;
	while(m--) {
		cin >> ui >> vi, --ui, --vi;
		adj[ui].push_back(vi);
	}
	for(int i=0; i<n; ++i)
		ans=max(cdp(i), ans);
	cout << ans-1;
}