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:
import java.util.*;

public class Main
{

    public static void main(String[] args)
    {
	    Scanner scanner = new Scanner(System.in);

	    String[] numbers = new String[scanner.nextInt()];
	    scanner.nextLine();
	    for (int i = 0; i < numbers.length; i++)
        {
            numbers[i] = scanner.nextLine();
        }

	    ArrayList<String> roundNumberComposition = calcCompositionOfRoundNumbers(numbers);

	    for (String element : roundNumberComposition)
        {
            System.out.println(element);
        }

	    scanner.close();
    }

    private static ArrayList<String> calcCompositionOfRoundNumbers(String[] numbers)
    {
        ArrayList<String> roundNumberComposition = new ArrayList<>();
        for (int i = 0; i < numbers.length; i++)
        {
            int number = Integer.parseInt(numbers[i]);
            StringBuilder roundNumbers = new StringBuilder();
            int counter = 0;
            int zeroCounter = 0;
            while (number > 0)
            {
                int digit = (number % 10);
                int roundNumber = digit * ((int) Math.pow(10, counter));
                if (roundNumber != 0)
                {
                    roundNumbers.append(roundNumber).append(" ");
                }
                else
                {
                    zeroCounter++;
                }
                counter++;
                number /= 10;
            }
            roundNumberComposition.add((counter - zeroCounter) + "");
            roundNumberComposition.add(roundNumbers.toString());
        }
        return roundNumberComposition;
    }
}