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.io.*;
import java.util.*;
public class Main 
{
    public static void main(String[] args)
    {
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        for(int j=0;j<t;j++)
        {
            ArrayList<Integer> arr=new ArrayList<Integer>(); 
            int n=sc.nextInt();
            String s=n+"";
            int flag=0;
            int i=0;
            while(i+1<s.length()&&s.length()>=0)
            {
                if(s.startsWith("0"))
                {
                    s=s.substring(1);
                    continue;
                }
                //System.out.println(s);
                String a = s;
                String b=s.substring(i+1);  
                s=s.substring(i+1);
                int c=Integer.parseInt(a);
                int d=Integer.parseInt(b);  
                if(c!=0&&d!=0&&c-d==0)
                {
                    flag=1;
                    arr.add(c);
                    break;
                }
                if(c-d<c)
                 arr.add(c-d);
                if(c-d==c)
                {
                    arr.add(c);
                    flag=1;
                    break;
                }
            }       
           if(flag!=1&&s.charAt(s.length()-1)!='0')
           { 
               
                arr.add(Integer.parseInt(s));
           }
           System.out.println(arr.size());
            
            for(int k=0;k<arr.size();k++)
            {
                System.out.print(arr.get(k)+" ");
            }
            System.out.println(); 
        }
       
    }
}