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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.util.regex.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    
	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc= new Scanner(System.in);
	    int t=sc.nextInt();
	    while(t>0){
	        int n= sc.nextInt();
	        int l=0;
	        ArrayList<Integer> arr= new ArrayList<>();
	        if(n<=9){
	            System.out.println("1");
	            System.out.println(n);
	            t--;
	            continue;
	        }
	        else if(n==10000){
	            System.out.println("1");
	            System.out.println(n);
	            t--;
	            continue;
	        }
	        int i=1000;
	        while(i>=1){
	            arr.add(n/i);
	            if(n/i!=0){
	                l++;
	            }
	            n=n-(n/i)*i;
	            i=i/10;
	        }
	        
	        System.out.println(l);
	        for(int j=0;j<arr.size();j++){
	            if(arr.get(j)!=0){
	                System.out.print(arr.get(j)*(int)Math.pow(10,arr.size()-j-1)+" ");
	            }
	        }
	        System.out.println();
	        t--;
	    }
	   
	    }
	    	// your code goes here
	}