**3 人解决**，6 人已尝试。

**10 份提交通过**，共有 38 份提交。

**8.6** EMB 奖励。

**单点时限: **2.0 sec

**内存限制: **256 MB

Chief Judge’s log, stardate 48642.5. We have decided to make a problem from elementary number theory. The problem looks like finding all prime factors of a positive integer, but it is not.

A positive integer whose remainder divided by 7 is either 1 or 6 is called a 7N+{1,6} number. But as it is hard to pronounce, we shall call it a **Monday-Saturday number.**

For **Monday-Saturday** numbers a and b, we say a is a **Monday-Saturday** divisor of b if there exists a **Monday-Saturday** number x such that ax = b. It is easy to show that for any **Monday-Saturday** numbers a and b, it holds that a is a **Monday-Saturday** divisor of b if and only if a is a divisor of b in the usual sense.

We call a **Monday-Saturday** number a **Monday-Saturday** prime if it is greater than 1 and has no **Monday-Saturday** divisors other than itself and 1. A **Monday-Saturday** number which is a prime in the usual sense is a **Monday-Saturday** prime but the converse does not always hold. For example, 27 is a **Monday-Saturday** prime although it is not a prime in the usual sense. We call a **Monday-Saturday** prime which is a **Monday-Saturday** divisor of a **Monday-Saturday** number a a **Monday-Saturday** prime factor of a. For example, 27 is one of the **Monday-Saturday** prime factors of 216, since 27 is a **Monday-Saturday** prime and 216 = 27 × 8 holds.

Any **Monday-Saturday** number greater than 1 can be expressed as a product of one or more **Monday-Saturday** primes. The expression is not always unique even if differences in order are ignored. For example, 216 = 6 × 6 × 6 = 8 × 27 holds.

Our contestants should write a program that outputs all **Monday-Saturday** prime factors of each input **Monday-Saturday** number.

The input is a sequence of lines each of which contains a single Monday-Saturday number. Each Monday-Saturday number is greater than 1 and less than 300000 (three hundred thousand). The end of the input is indicated by a line containing a single digit 1.

For each input Monday-Saturday number, it should be printed, followed by a colon `:’ and the list of its Monday-Saturday prime factors on a single line. Monday-Saturday prime factors should be listed in ascending order and each should be preceded by a space. All the Monday-Saturday prime factors should be printed only once even if they divide the input Monday-Saturday number more than once.

Input

205920 262144 262200 279936 299998 1

Output

205920: 6 8 13 15 20 22 55 99 262144: 8 262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185 279936: 6 8 27 299998: 299998

**3 人解决**，6 人已尝试。

**10 份提交通过**，共有 38 份提交。

**8.6** EMB 奖励。

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