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.io.*;
import java.util.*;

public class Main {
	FastScanner in = new FastScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	
	public void run() {
		HashSet<Integer> hash = new HashSet<Integer>();
		ArrayList<Integer> prime = new ArrayList<Integer>();
		for (int i = 7; i <= 300000; i += 7) {
			for (int dx = -1; dx <= 1; dx += 2) {
				if (!hash.contains(i+dx)) {
					prime.add(i+dx);
					for (int j = i+dx; j <= 300000; j += i+dx) 
						hash.add(j);
				}
			}
		}
		while (true) {
			int n = in.nextInt();
			if (n == 1) break;
			
			ArrayList<Integer> res = new ArrayList<Integer>();
			for (int p : prime) {
				if (n % p == 0) {
					res.add(p);
				}
			}
			
			System.out.print(n + ":");
			for (int i = 0; i < res.size(); i++) {
				int x = res.get(i);
				System.out.print(" " + x);
			}
			System.out.println();
		}
		out.close();
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}