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.*;

public class Main {
	//static List<Integer> primenumbers;
	public static void main(String[] args) {
		Scanner stdin = new Scanner(System.in);
		//setPrimeNumbers(300000);
		while(stdin.hasNext()) {
			int n = stdin.nextInt();
			if (n == 1) break;
			Iterator it = calculateMSPF(n).iterator();
			System.out.print(n + ": ");
			if (! it.hasNext()) System.out.print(n);
			while (it.hasNext()) {
				System.out.print(Integer.parseInt(it.next().toString()));
				if (it.hasNext()) System.out.print(" ");
			}
			System.out.println("");
		}
		System.exit(0);
	}

	/*public static void setPrimeNumbers(int n) {
		BitSet isntprime = new BitSet(n);
		isntprime.set(0, true);
		isntprime.set(1, true);
		for ()
	}*/

	public static boolean isMSNumber(int n) {
		int d = n % 7;
		return d == 1 || d == 6;
	}

	public static boolean isMSPrime(int n) {
		if (! isMSNumber(n)) return false;
		return calculateMSDivisors(n).size() == 2;
	}

	public static List<Integer> calculateDivisors(int n) {
		List<Integer> ds = new ArrayList<Integer>();
		for (int i = 1; i <= n / 2; i++) {
			if (n % i == 0) ds.add(i);
		}
		ds.add(n);
		return ds;
	} 

	public static List<Integer> calculateMSDivisors(int n) {
		List<Integer> msds = new ArrayList<Integer>();
		Iterator it = calculateDivisors(n).iterator();
		while (it.hasNext()) {
			int d = Integer.parseInt(it.next().toString());
			if (isMSNumber(d)) msds.add(d);
		}
		return msds;
	}

	public static List<Integer> calculateMSPF(int n) {
		List<Integer> mspfs = new ArrayList<Integer>();
		Iterator it = calculateMSDivisors(n).iterator();
		while (it.hasNext()) {
			int msd = Integer.parseInt(it.next().toString());
			if (isMSPrime(msd)) mspfs.add(msd);
		}
		return mspfs;
	}
}