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B. Maths

Time limit: 1.0 second
Memory limit: 64 MB
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.

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 a1, …, an (1 ≤ ai ≤ 300).

Sample

inputoutput
```3
```
```1 3 4
```
Problem Author: folklore, prepared by Alexander Ipatov
Problem Source: Ural Sport Programming Championship 2015
To submit the solution for this problem go to the Problem set: 2047. Maths