Top Two Teams by Points, Then Goal Difference, Then Goals Scored

A league records four statistics for each of its `n` teams in four parallel arrays: `wins[i]`, `draws[i]`, `scored[i]` (goals scored) and `conceded[i]` (goals conceded) all describe team `i`. Rank the teams and return the indices of the first-placed and second-placed teams. A team earns 3 points for each win and 1 point for each draw, so team `i` has `points = 3 * wins[i] + draws[i]`. ### Function Signature ```python def top_two_teams(wins: list[int], draws: list[int], scored: list[int], conceded: list[int]) -> list[int]: ``` ### Rules Teams are ranked by the following keys, each one used only to break a tie in all of the previous keys: 1. More points ranks higher. 2. Greater goal difference, `scored[i] - conceded[i]`, ranks higher. 3. More goals scored, `scored[i]`, ranks higher. 4. The smaller index ranks higher. Return a list of exactly two indices, `[first, second]`. Because the last key never ties, the answer is unique. ### Constraints - `2 <= n <= 100000`, where `n` is the common length of all four arrays - `0 <= wins[i] <= 1000` and `0 <= draws[i] <= 1000` - `0 <= scored[i] <= 100000` and `0 <= conceded[i] <= 100000` - Goal difference can be negative. ### Examples **Example 1** - Input: `wins = [1, 3, 2, 3]`, `draws = [2, 0, 3, 0]`, `scored = [5, 7, 6, 9]`, `conceded = [5, 3, 5, 5]` - Output: `[3, 1]` - Explanation: Points are `[5, 9, 9, 9]`. Teams `1`, `2` and `3` tie on 9 points. Their goal differences are `4`, `1` and `4`, so team `2` drops behind. Teams `1` and `3` still tie, and team `3` scored more goals (9 against 7), so team `3` is first and team `1` is second. **Example 2** - Input: `wins = [2, 2]`, `draws = [1, 1]`, `scored = [4, 4]`, `conceded = [2, 2]` - Output: `[0, 1]` - Explanation: The two teams tie on every statistic, so the smaller index ranks higher. **Example 3** - Input: `wins = [0, 4, 3]`, `draws = [5, 0, 4]`, `scored = [2, 10, 3]`, `conceded = [1, 2, 3]` - Output: `[2, 1]` - Explanation: Points are `[5, 12, 13]`. Team `2` is first on points even though team `1` has the far better goal difference (8 against 0); goal difference only matters when points are equal.