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 a1, …, an
such that for any k from 2 to n the sum a1 + … + ak has exactly ak different positive divisors.
Help Vasya to cope with this task.
The only line contains an integer n (2 ≤ n ≤ 100 000).
If there is no such sequence output “Impossible”.
Otherwise output space-separated integers a1, …, an (1 ≤ ai ≤ 300).
Problem Author: folklore, prepared by Alexander Ipatov
Problem Source: Ural Sport Programming Championship 2015