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;

int n, m, a, b, inin[100005], dp[100005];
vector<int> G[100005];
queue<int> q;

int main() {
	cin >> n >> m;
	for (int i=0; i<m; i++) {
		cin >> a >> b;
		G[a].push_back(b);
		inin[b]++;
	}
	for (int i=1; i<=n; i++) {
		if (inin[i] == 0) q.push(i);
	}
	while(!q.empty()) {
		int u = q.front();
		q.pop();
		for (int v : G[u]) {
			inin[v]--;
			if (inin[v] == 0) q.push(v);
			dp[v] = max(dp[v], dp[u] + 1);
		}
	}
	cout << *max_element(dp, dp + n + 1) << endl;
}