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.awt.Point;
import java.io.FileInputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Scanner;
 
public class Main {
     
    static int num;
    static ArrayList<Integer> getsudo;
    static int[] ret;
    
    static void start()
    {
    	// 月土素因数探し
    	System.out.print(num + ":");
    	for (int i = 6; i <= num; i++) {
    		if( (i % 7) != 1 && (i % 7) != 6 ) continue;
    		if(ret[i] == 0) continue;
    		if(num % i == 0) System.out.print(" " + i);
		}
    	System.out.print("\n");
    }
     
    public static void main(String[] args)
    {
        Scanner sca = new Scanner(System.in);
        
        // 月土数作り
    	getsudo = new ArrayList<Integer>();
    	for (int i = 1; i <= 300000; i++) {
    		if( (i % 7) == 1 || (i % 7) == 6 ) getsudo.add(new Integer(i));
    	}
    	
    	// 月土素数作り
    	ret = new int[300000+1];
    	for (int i = 0; i < (300000+1); i++) ret[i] = 1;
    	ret[0] = ret[1] = 0;
    	int loop = (int)(Math.sqrt(300000) + 1);
    	for (int i = 2; i <= loop; i++) {
    		if( (i % 7) != 1 && (i % 7) != 6 ) continue;
    		if(ret[i] == 0) continue;
    		for (Integer j : getsudo) {
    			if(j == 1) continue;
    			if(300000 < i*j) break;
    			ret[i*j] = 0;
    		}
    	}
        
        while(true)
        {
        	num = sca.nextInt();
        	if(num == 1) break;
            
            start();
        }
        
    }
}