CF1408G Clusterization Counting

There are $ n $ computers in the company network. They are numbered from $ 1 $ to $ n $ . For each pair of two computers $ 1 \leq i < j \leq n $ you know the value $ a_{i,j} $ : the difficulty of sending data between computers $ i $ and $ j $ . All values $ a_{i,j} $ for $ i

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Here are all possible ways to separate all computers into $ 4 $ groups in the second example: - $ \{1, 2\}, \{3, 4\}, \{5\}, \{6, 7\} $ ; - $ \{1\}, \{2\}, \{3, 4\}, \{5, 6, 7\} $ ; - $ \{1, 2\}, \{3\}, \{4\}, \{5, 6, 7\} $ .