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.Scanner;
public class Pro14 {
	
	public static void main(String[] args) 
	{	   
		
		 Scanner sc = new Scanner (System.in);
		 int t =sc.nextInt();
          
		  for(int j =0;j<t;j++)
		  {
			
			  int n  =sc.nextInt();
			   int i =0; 
			   int count =0;
			  int a =n;
			  while(a!=0)
			  {
				   int rem =a%10;   
				     if(rem!=0)
				  count++;
				     
				  
				   a=a/10;
			  }
			   System.out.println(count);
			  while(n!=0)
			  {
				   int rem =n%10;   
				     if(rem!=0){
				   int res = (int) (rem*Math.pow(10, i));
				   System.out.print(res+" ");
				     }
				   i++;
				   n=n/10;
			  }
			  System.out.println();
			  
		  }
	}
}