Willson the Canada Goose is like any other Canada Goose - he suspects that many humans don't like him.

As a result, he challenges you to do the following problem:

Consider the set .

We say that an element in is a **unit** if there is some element in with .

We say that a non-zero, non-unit element in is **irreducible** if there are no elements in where are not units and .

We say that a non-zero, non-unit element in is **prime** if for all elements in , if for some element in , then for some element in or for some element in .

Given , please output all of the units, irreducibles, and primes of .

#### Input Specification

The only line of input will contain a single integer, .

For of the points, is prime.

For an additional of the points, .

For an additional of the points, .

#### Output Specification

Output, in numerical order, first the units, then the irreducibles, then the primes of . See the Sample Output for more specific formatting.

#### Sample Input 1

`10`

#### Sample Output 1

```
Units:
1
3
7
9
Irreducibles:
Primes:
2
4
5
6
8
```

#### Sample Input 2

`12`

#### Sample Output 2

```
Units:
1
5
7
11
Irreducibles:
2
10
Primes:
2
3
9
10
```

## Comments