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;
using ll = long long;

vector<int> v[101010];

int dp[101010];

int search(int x) {
	if (dp[x]) return dp[x]+1;
	int r = 0;
	for (auto c : v[x]) {
		r = max(r, search(c));
	}
	dp[x] = r;
	return r+1;
}

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

	int n, m;
	cin >> n >> m;

	for (int i = 0; i < m; ++i) {
		int a, b;
		cin >> a >> b;

		v[a].push_back(b);
	}
	int mx = 0;
	for (int i = 1; i <= n; ++i) mx = max(mx, search(i) - 1);
	cout << mx << '\n';
}