Problem: A positive (strictly greater than zero) integer is called round if it is of the form d00...0. In other words, a positive integer is round if all its digits except the leftmost (most significant) are equal to zero. In particular, all numbers from 1 to 9 (inclusive) are round.

For example, the following numbers are round: 4000, 1, 9, 800, 90. The following numbers are not round: 110, 707, 222, 1001.

You are given a positive integer n (1 ≤ n ≤ 10^4). Represent the number n as a sum of round numbers using the minimum number of summands (addends). In other words, you need to represent the given number n as a sum of the least number of terms, each of which is a round number.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.

Each test case is a line containing an integer n (1 ≤ n ≤ 10^4).

Output

Print t answers to the test cases. Each answer must begin with an integer k — the minimum number of summands. Next, k terms must follow, each of which is a round number, and their sum is n. The terms can be printed in any order. If there are several answers, print any of them.

Example

Input


5
5009
7
9876
10000
10


Output


2
5000 9
1
7 
4
800 70 6 9000 
1
10000 
1
10 

Solution (in JAVA):

Solution:
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import java.util.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		
		while(n-- > 0)
		{
		    int num = sc.nextInt();
		    PrintIsRound(num);
		}
	}
	
	static void PrintIsRound(int n)
	{
	    int count = 1;
	    HashSet<Integer> hs = new HashSet<Integer>();
	    while(!IsRound(n))
	    {
	        int rem = ExtractNonZero(n);
	        hs.add(rem);
	        n -= rem;
	        count++;
	    }
	    hs.add(n);
	    
	    System.out.print(count);
	    System.out.println();
	    
	    Iterator it = hs.iterator();
	    while(it.hasNext())
	    {
	        System.out.print(it.next() + " ");
	    }
	    System.out.println();
	}
	
	static boolean IsRound(int n)
	{
	    if(n <= 10)
	        return true;
	        
        String temp = Integer.toString(n);
        int[] arr = new int[temp.length()];
        for (int i = 0; i < temp.length(); i++)
        {
            arr[i] = temp.charAt(i) - '0';
        }
        int count = 0;
        
        for(int i = 0 ; i < arr.length ; i++)
        {
            if(arr[i] != 0)
                count++;
            if(count > 1)
                return false;
        }
        
        return true;
	}
	
	static int ExtractNonZero(int n)
	{
	    
	    String temp = Integer.toString(n);
        int[] arr = new int[temp.length()];
        for (int i = 0; i < temp.length(); i++)
        {
            arr[i] = temp.charAt(i) - '0';
            
        }
        
        int i = arr.length - 1;
        while(i >= 0)
        {
            if(arr[i] != 0)
                break;
            i--;
        }
        
        int power = (arr.length - 1) - i;
        int num = arr[i];
        
        int multiplier = (int) Math.pow(10, power);
        return num * multiplier;
	}
	  
}