On Lineland there are 2018 bus stations numbered 1 through 2018 from left to right. A self-driving bus that can carry at most $N$ passengers starts from station 1 and drives all the way to station 2018, while making a stop at each bus station. Each passenger that gets on the bus at station $i$ will get off at station $j$ for some $j>i$ (the value of $j$ may vary over different passengers). Call any group of four distinct stations $i_1, i_2, j_1, j_2$ with $i_u< j_v$ for all $u,v\in \{1,2\}$ a [i]good[/i] group. Suppose that in any good group $i_1, i_2, j_1, j_2$, there is a passenger who boards at station $i_1$ and de-boards at station $j_1$, or there is a passenger who boards at station $i_2$ and de-boards at station $j_2$, or both scenarios occur. Compute the minimum possible value of $N$.

[i]Proposed by Yannick Yao[/i]
**
   - We need to find the minimum \( N \) such that every possible good group is covered.
   - Consider the worst-case scenario where each passenger covers a unique pair \((i, j)\). The total number of such pairs is given by the binomial coefficient \( \binom{2018}{2} \).

4. **Calculating the Minimum \( N \):**
   - The number of ways to choose 2 stations out of 2018 is:
     \[
     \binom{2018}{2} = \frac{2018 \times 2017}{2} = 2037173
     \]
   - However, we need to ensure that for any four stations \( i_1, i_2, j_1, j_2 \), there is a passenger covering either \( (i_1, j_1) \) or \( (i_2, j_2) \).
   - This implies that we need to cover all possible pairs \((i, j)\) with the minimum number of passengers.

5. **Finding the Minimum \( N \):**
   - To cover all possible pairs, we need to ensure that each pair is covered by at least one passenger.
   - The minimum number of passengers required to cover all pairs can be found by considering the maximum number of pairs a single passenger can cover.
   - Each passenger can cover pairs from their boarding station to any de-boarding station after it.

6. **Conclusion:**
   - The minimum number of passengers \( N \) required to ensure that every good group is covered is:
     \[
     N = 1009
     \]
   - This is because each passenger can cover pairs from their boarding station to any de-boarding station after it, and we need to ensure that all pairs are covered.

The final answer is \( \boxed{1009} \).