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.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;


public  class FibinacciSeries 
{

	   
	   static class FastReader 
	    { 
	        BufferedReader br; 
	        StringTokenizer st; 
	       
	  
	        public FastReader() 
	        { 
	            br = new BufferedReader(new
	                     InputStreamReader(System.in)); 
	        } 
	  
	        String next() 
	        { 
	            while (st == null || !st.hasMoreTokens()) 
	            { 
	                try
	                { 
	                    st = new StringTokenizer(br.readLine()); 
	                } 
	                catch (IOException  e) 
	                { 
	                    e.printStackTrace(); 
	                } 
	            } 
	            return st.nextToken();
	            
	        } 
	  
	        int nextInt() 
	        { 
	            return Integer.parseInt(next()); 
	        } 
	  
	        long nextLong() 
	        { 
	            return Long.parseLong(next()); 
	        } 
	  
	        double nextDouble() 
	        { 
	            return Double.parseDouble(next()); 
	        } 
	  
	        String nextLine() 
	        { 
	            String str = ""; 
	            try
	            { 
	                str = br.readLine(); 
	            } 
	            catch (IOException e) 
	            { 
	                e.printStackTrace(); 
	            } 
	            return str; 
	        }

			public Character charAt(int i) {
				// TODO Auto-generated method stub
				return null;
			} 
	    } 

  

	  // Complete the hurdleRace function below.
//    public static void solve() {
//    	FastReader s=new FastReader();

   
    public static void main(String[] args) throws IOException {
    	FastReader s=new FastReader();
    	int t = s.nextInt();
    	
    	
    	
	    for(int j=0;j<t;j++) {
	    	int n = s.nextInt();
	    	int c=0;
	    	List<Integer> ar =new ArrayList<>();
	    	int p=1;
	    	while(n>0){
	    			if(n%10!=0)ar.add(n%10*p);
	    			p *=10;
	    			n/=10;
	    			
	    		}
	    		
	    	System.out.println(ar.size());
	    	for(int i=0;i<ar.size();i++) {
	    		System.out.print(ar.get(i) + " ");
	    	}
	    	System.out.println();
	    }	
    	
    	
    	
    	
    }	
    
}