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 HashMap<Integer, Numnum> map;
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		map = new HashMap<Integer, Numnum>();
		boolean[] swm = new boolean[300001];
		boolean[] swm2 = new boolean[300001];
		for(int i=1;i<=300000;i++){
			if(i%7==1||i%7==6){
				swm[i]=true;
				swm2[i]=true;
			}
		}
		for (int i = 7; i <= 299999; i += 7) {
			Numnum num1 = new Numnum(i - 1);
			Numnum num2 = new Numnum(i + 1);

			for (int j = 2; num1.mynum * j <= 300000; j++) {
				swm[num1.mynum * j] = swm[num1.mynum * j] ? false :swm[num1.mynum*j];
			}
			for (int j = 2; num2.mynum * j <= 300000; j++) {
				swm[num2.mynum * j] = swm[num2.mynum * j] ? false :swm[num2.mynum*j];
			}

			map.put(num1.mynum, num1);
			map.put(num2.mynum, num2);
		}
		
		for (int i = 6; i <= 300000; i ++) {
			if(swm[i])map.get(i).set.add(i);
			if(!swm[i])continue;
			for (int j = 2; i * j <= 300000; j++) {
				if(swm2[i*j]){
					map.get(i*j).set.add(i);
					if(swm[j])map.get(i*j).set.add(j);
				}
			}
		}

		while (true){
			int n = sc.nextInt();
			if (n == 1)
				break;
			System.out.print(n + ":");
			for (int result : map.get(n).set) {
				if (swm[result])System.out.print(" " + result);
			}
			System.out.println();
		}

	}
}

class Numnum {
	int mynum;
	TreeSet<Integer> set = new TreeSet<Integer>();
	public Numnum(int num) {
		mynum = num;
	}
	
}