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 class Program1 {
    
    public static void main(String[] args) {
        
        int[] POWERSOF10 = {1, 10, 100, 1000, 10000};
        
        Scanner scanner = new Scanner(System.in);

        int t = scanner.nextInt();        
        
        for (int i = 0; i<t; i++) {
            int n = scanner.nextInt();
            
            int count = 0;
            int[] outputs = new int[5];
            
            for (int j = 4; j >= 0; j--) {                
                int result = n / POWERSOF10[j];
                
                if (result > 0) {
                    count++;
                    result *= POWERSOF10[j];
                    outputs[count] = result;
                    n -= result;
                }
            }            
            
            System.out.println(count);
            for (int k = 1; k <= count; k++) {
                if (outputs[k] > 0) {
                    System.out.print(outputs[k]);
                    if (k < count) {                       
                        System.out.print(" ");
                    }
                }
            }            
            System.out.println();
        }        
    }
}