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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;
 
 
    
    public class Solution{ 
        public static void function(int n)
        {
            ArrayList<Integer> Arr=new ArrayList<>();
            String  S=String.valueOf(n);
            int x=1;
            for(int i=S.length()-1;i>=0;i--)
            {
                int P=Character.getNumericValue(S.charAt(i))*x;
                 x=x*10;
                if(P==0)
                {
                    continue;
                }
                else
                {
                   Arr.add(P);
                }
               
                
            }
            System.out.println(Arr.size());
            for(int i=0;i<Arr.size();i++)
            {
                System.out.print(Arr.get(i)+" ");
            }
           
        }
      
   public static void main (String[] args)  throws IOException{
	Scanner sc=new Scanner(System.in);
	    int T=0;
	    if(sc.hasNextInt())
	    {
	        T=sc.nextInt();
	    }
	    for(int t=0;t<T;t++)
            {
	        int N=0;
	        if(sc.hasNextInt())
	        {
	            N=sc.nextInt();
	        }
                function(N);
                System.out.println();
	      
	      
	 
	        
	    }
       
   }
    }