31385번 - Maths 스페셜 저지다국어

문제

Android Vasya attends Maths classes. His group started to study the number theory recently. The teacher gave them several tasks as a homework. One of them is as follows.

There is an integer $n$. The problem is to find a sequence of integers $a_1, \ldots, a_n$ such that for any $k$ from 2 to $n$ the sum $a_1 + \ldots + a_k$ has exactly $a_k$ different positive divisors. Help Vasya to cope with this task.

입력

The only line contains an integer $n$ (2ドル \leq n \leq 100,000円$).

출력

If there is no such sequence output Impossible. Otherwise output space-separated integers $a_1, \ldots, a_n$ (1ドル \leq a_i \leq 300$).

제한

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