P14034 [PAIO 2025] Cards

**DO NOT** include `cards.h`. Submit using C++ >=17.

You have $X$ black, $Y$ white, and $Z$ cyan cards (total $X + Y + Z$). You will play all the cards one by one onto a single pile in any order you choose. After you place each card, check the pile: * If the pile (now) contains at least one card of each of the three colors, you score 1 point, then all cards **except the one you just played** are destroyed (removed from the pile). The card you just played remains as the only card on the pile. * Otherwise, nothing happens. Your task is to calculate the maximum score you can get. ### Implementation Details You need to implement one procedure called `maximum_score`: ```cpp int64 maximum_score(int32 X, int32 Y, int32 Z); ``` * $X$: the number of black cards; * $Y$: the number of white cards; * $Z$: the number of cyan cards; * This procedure might be called no more than 100 times for each test case at the beginning of the program. The procedure should return the maximum score you can get.

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### Examples #### Example 1 Consider the following call. ```cpp maximum_score(2, 2, 1); ``` The procedure should return 2. #### Example 2 Consider the following call. ```cpp maximum_score(4, 3, 4); ``` The procedure should return 5. ### Sample Grader The sample grader reads the input in the following format: * Line 1: An integer $T$, indicating the number of calls to `maximum_score` * Next $T$ lines: Three integers $X, Y,$ and $Z$ The sample grader calls `maximum_score(X, Y, Z)` and prints the returned value. ### Constraints * $1 \le X \le 10^9$ * $1 \le Y \le 10^9$ * $1 \le Z \le 10^9$ ### Scoring 1. Subtask 1 (4 points): $X = Y = Z = 1$ 2. Subtask 2 (7 points): $X + Y + Z \le 8$ 3. Subtask 3 (15 points): $X + Y + Z \le 16$ 4. Subtask 4 (25 points): $X, Y, Z \le 50$ 5. Subtask 5 (12 points): $X = Y = Z$ 6. Subtask 6 (24 points): $X < Y = Z$ 7. Subtask 7 (13 points): No additional constraints