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.Scanner;

public final class CodeForces {

    private static void solution(String[] inputs) {
        for(String input : inputs) {
            int divider = (int)Math.pow(10, input.length() - 1);
            int value = Integer.parseInt(input);
            int count = 0;
            StringBuilder builder = new StringBuilder();
            while(divider >= 10 && value != 0) {
                if(value/divider != 0){
                    count++;
                    builder.append((value/divider) * divider).append(" ");
                }
                value = value % divider;
                divider = divider/10;
            }
            if(value != 0) {
                count ++;
                builder.append(value);
            }
            System.out.println(count);
            System.out.println(builder.toString());
        }
    }

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

        try {
            int count = Integer.parseInt(in.nextLine());
            String[] inputs = new String[count];
            for(int i = 0; i < count; ++i) {
                inputs[i] = in.nextLine();
            }
            in.close();
            solution(inputs);
        }
        catch(Exception e) {
            System.out.println(e.getStackTrace());
        }
    }
}