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.lang.*;
import java.io.*;

public class SumofRoundNumbers
{
   
	public static void main (String[] args) throws java.lang.Exception
	{
        Scanner s = new Scanner(System.in);
	    int t=s.nextInt();
	    while(t-->0){
	        int n=s.nextInt();
	        int count=0;
	        int[] arr=new int[6];
	        int i=0;
	        while(n>0){
	            int rem=(n%10)*(int)Math.pow(10,i);
	            if(rem>0){
    	            arr[count]=rem;
    	            count++;
	            }
	            n=n/10;
	            i++;
	        }
	        System.out.println(count);
	        for(int j=0;j<count;j++){
	            System.out.print(arr[j]+" ");
	        }
	        System.out.println();
	    }
	}
}