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 CodeforcesConesttDiv4Problem1 {
    
    public static void main(String[] args) {
        
        Scanner input = new Scanner(System.in);
        int line = input.nextInt();
        for (int i = 0; i < line; i++) {
            int number = input.nextInt();
            
            int count =0;
            int zero=0;
            
            
            String s1 = Integer.toString(number);
            char[] string1  =s1.toCharArray();
            int length1 = string1.length;
            for (int j = 0; j <length1; j++) {
                
                if(string1[j]=='0'){
                    zero++;
                }
            }
            
            int length2 = length1-zero;
            System.out.println(length2);
            
            
            
            for(int j=0;j<length1;j++)
            {
                count=0;
                if(string1[j]!='0')
                {
                    System.out.print(string1[j]);
                    while(count<length1-j-1)
                            {
                                System.out.print("0");
                                count++;
                            }
                    
                     System.out.print(" ");   
                    
                }
                  
                }
           
          
            System.out.println();
        }
    }
    
}