Maths

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.

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

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