围栏 - Problème

#5944. 围栏

Statistiques

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

在本题中，你需要求出在 $N \times M$ 的矩形网格（$N$ 条水平线段和 $M$ 条垂直线段）上放置石子，以围住至少 $K$ 个交点所需的最少石子数量。如果满足以下任一条件，则称一个交点被围住：

该点上放置了一颗石子。
从该点出发，无法仅通过空闲的交点沿网格线到达网格边界上的空闲点。

例如，在 $4 \times 5$ 的网格中围住 $8$ 个点，至少需要 $6$ 颗石子。下图展示了其中一种合法的石子布局，被围住的点用 "x" 标记。

样例

输入格式 1

2
4 5 8
3 5 11

输出格式 1

Case #1: 6
Case #2: 8

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