hackercupai/hackercup huggingface dataset:
Four friends are playing a card game with two teams of two players each. Team \(A\) consists of players \(A1\) and \(A2\) while team \(B\) consists of players \(B1\) and \(B2\).

There is a deck of \(N\) cards (where \(N\) is always a multiple of \(4\)), numbered from \(1\) to \(N\), with all cards visible to all players at all times. First, the cards are dealt out evenly to each player:
- Player \(A1\) has cards \(A1_1\), ..., \(A1_{N/4}\).
- Player \(B1\) has cards \(B1_1\), ..., \(B1_{N/4}\).
- Player \(A2\) has cards \(A2_1\), ..., \(A2_{N/4}\).
- Player \(B2\) has cards \(B2_1\), ..., \(B2_{N/4}\).

The game proceeds for \(N/4\) rounds. In each round, each player plays a card. Player \(A1\) plays first, then player \(B1\), then player \(A2\), then player \(B2\). A player may choose to play any of their cards when it’s their turn. After all four players have played a card, the team who played the highest card will score \(1\) point. Once a round is complete, the four played cards are removed from the game, and then the next round starts. This continues until all cards have been played.

For example, the first round of the second sample case might be played as follows, with player \(B2\) winning a point for team \(B\):

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Assuming each team plays to maximize its score, how many points will team \(A\) score?

# Constraints

\(1 \le T \le 500\)
\(4 \le N \le 4{,}000{,}000\)
\(N\) is a multiple of \(4\).
Each card from \(1\) to \(N\) is guaranteed to exist in exactly one player’s hand.

The sum of \(N\) across all test cases is at most \(5{,}000{,}000\).

# Input Format

Input begins with a single integer \(T\), the number of test cases. For each test case, there is first a line containing a single integer \(N\). Then there are \(4\) lines containing the players' cards:
- Line 1: \(N/4\) space-separated integers, \(A1_1, ..., A1_{N/4}\).
- Line 2: \(N/4\) space-separated integers, \(B1_1, ..., B1_{N/4}\).
- Line 3: \(N/4\) space-separated integers, \(A2_1, ..., A2_{N/4}\).
- Line 4: \(N/4\) space-separated integers, \(B2_1, ..., B2_{N/4}\).

# Output Format

For the \(i\)th test case, output a line containing `"Case #i: "` followed by a single integer, the number of points that team \(A\) will score.

# Sample Explanation

In the first case, one possible way the cards can be played optimally is:
- Round 1: \([2, 7, \textbf{8}, 5]\)
- Round 2: \([1, 3, \textbf{6}, 4]\)

Team \(A\) will score \(2\) points, and team \(B\) can do no better by playing differently.

In the second case, one possible way the cards can be played optimally is:

- Round 1: \([1, 6, 2, \textbf{9}]\)
- Round 2: \([\textbf{13}, 5, 3, 8]\)
- Round 3: \([12, 15, \textbf{16}, 10]\)
- Round 4: \([\textbf{14}, 7, 4, 11]\)

Team \(A\) will score \(3\) points.

In the third case, one possible way the cards can be played optimally is:

- Round 1: \([11, \textbf{12}, 9, 4]\)
- Round 2: \([13, 2, 8, \textbf{14}]\)
- Round 3: \([6, 1, 5, \textbf{10}]\)
- Round 4: \([15, \textbf{16}, 7, 3]\)

Team \(B\) can always prevent team \(A\) from scoring any points.