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;
#define N 100005
vector<int> G[N];
int _dp[N];
int dp(int v) {
	if (~_dp[v]) return _dp[v];
	int rt = 0;
	for (int u : G[v]) {
		rt = max(rt, dp(u) + 1);
	}
	return (_dp[v] = rt);
}
int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	int n, m;
	cin >> n >> m;
	while (m--) {
		int u, v;
		cin >> u >> v;
		G[v].push_back(u);
	}
	for (int i = 1 ; i <= n ; ++i) {
		G[0].push_back(i);
		_dp[i] = -1;
	}
	_dp[0] = -1;
	cout << dp(0) - 1 << '\n';
}