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, …, a_n such that for any k from 2 to n the sum a₁ + … + a_k has exactly a_k 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, …, a_n (1 ≤ a_i ≤ 300).