CF453B Little Pony and Harmony Chest

Description

Princess Twilight went to Celestia and Luna's old castle to research the chest from the Elements of Harmony. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF453B/8ef25b8d7e467d01f853452542bae72c04218a5c.png)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: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF453B/97bad96a3a07ca00d2975bfabd2fb8b2f2ff6370.png)You are given sequence $ a_{i} $ , help Princess Twilight to find the key.

Input Format

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Output Format

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