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 <iostream>
#include <vector>
using namespace std;

const int maxn = 1e5;
vector<int> adj[maxn + 1];
int dp[maxn + 1] = {0};

int dfs(int x) {
  int &m = dp[x];
  if (m) return m;
  for (int y : adj[x]) m = max(m, dfs(y) + 1);
  return m;
}
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 0, x, y; i < m; i++) {
    cin >> x >> y;
    adj[x - 1].push_back(y - 1);
  }
  for (int i = 0; i < n; i++)
    adj[n].push_back(i);
  cout << dfs(n) - 1 << '\n';
}