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}, …, *a*_{n}
such that for any *k* from 2 to *n* the sum *a*_{1} + … + *a*_{k} has exactly *a*_{k} different positive divisors.
Help Vasya to cope with this task.

### Input

The only line contains an integer *n* (2 ≤ *n* ≤ 100 000).

### Output

If there is no such sequence output “Impossible”.
Otherwise output space-separated integers *a*_{1}, …, *a*_{n} (1 ≤ *a*_{i} ≤ 300).

### Sample

**Problem Author: **folklore, prepared by Alexander Ipatov

**Problem Source: **Ural Sport Programming Championship 2015