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.*;
import java.io.*;
public class Round
{
	public static void main(String[] args)throws Exception
	{
	    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    PrintWriter pw=new PrintWriter(System.out);
	    int t=Integer.parseInt(br.readLine());
	    while(t-->0)
	    {
	        int n=Integer.parseInt(br.readLine());
	        int Dig=0;
	        int n1=n;
	        int ct=0;
	        ArrayList<Integer> al=new ArrayList<Integer>();
	        while(n1!=0)
	        {
	            int x=n1%10;
	            Dig+=1;
	            if(x!=0)
	            {
	                int x2=(int)((Math.pow(10,Dig-1))*x);
	                //pw.print(x2+" ");
	                Integer Int=new Integer(x2);
	                al.add(Int);
	                ct++;
	            }
	            n1=n1/10;
	        }
	        pw.println(ct);
	        for(int i:al)
	        {
	            pw.print(i+" ");
	        }
	        pw.println();
	        
	        
	        
	    }
	    pw.flush();
	}
}