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.

Input

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.

Output

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.

Sample Input


205920
262144
262200
279936
299998
1


Output for the Sample Input


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






Example

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
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		Main instance = new Main();
		instance.init(300000);
		read().stream().map(instance::execute).forEach(System.out::println);
	}

	private static List<Integer> read() {
		List<Integer> list = new ArrayList<>();
		Scanner sc = new Scanner(System.in);
		while (true) {
			int nextVal = sc.nextInt();
			if (nextVal == 1) {
				break;
			}
			list.add(nextVal);
		}
		sc.close();
		return list;
	}

	private List<Integer> mondaySaturdayList = new ArrayList<>();
	private List<Integer> mondaySaturdayPrimeList = new ArrayList<>();

	public void init(int maxValue) {
		int i;
		boolean isMonday;
		for (i = 1, isMonday = true; i < maxValue;) {
			if (isMonday) {
				i = i + 5;
				isMonday = false;
			} else {
				i = i + 2;
				isMonday = true;
			}
			mondaySaturdayList.add(i);
		}
		IntStream primeStream = mondaySaturdayList.stream().mapToInt(num -> num);
		for (int j : mondaySaturdayList) {
			if (j * j > maxValue) {
				break;
			}
			primeStream = primeStream.filter(num -> num <= j || num % j != 0);
		}
		mondaySaturdayPrimeList = primeStream.boxed().collect(Collectors.toList());
	}

	public String execute(int value) {
		StringBuilder sb = new StringBuilder(String.valueOf(value));
		sb.append(": ");
		sb.append(getPrimeFactors(value).stream().map(String::valueOf).collect(Collectors.joining(" ")));
		return sb.toString();
	}

	private List<Integer> getPrimeFactors(int value) {
		List<Integer> primeFactors = new ArrayList<>();
		for (Integer prime : mondaySaturdayPrimeList) {
			if (value > prime && value % prime == 0) {
				primeFactors.add(prime);
			}
		}
		if (primeFactors.isEmpty() && (value % 7 == 1 || value % 7 == 6)) {
			primeFactors.add(value);
		}
		return primeFactors;
	}
}