CF453B Little Pony and Harmony Chest

Princess Twilight went to Celestia and Luna's old castle to research the chest from the Elements of Harmony. A sequence of positive integers $ b_{i} $ is harmony if and only if for every two elements of the sequence their greatest common divisor equals 1. According to an ancient book, the key of the chest is a harmony sequence $ b_{i} $ which minimizes the following expression: You are given sequence $ a_{i} $ , help Princess Twilight to find the key.

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