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.*;
public class sum_of_round_numbers {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		int t=in.nextInt();
		while(t!=0)
		{
			int n=in.nextInt(),c=0;
			String s="";
			for(int i=0;i<String.valueOf(n).length();i++)
			{
				if(String.valueOf(n).charAt(i)!='0')
				{
					c++;
				}
				if(i==0)
				{
					s=s+'1';
				}
				else
				{
					s=s+'0';
				}
			}
			System.out.println(c);
	        while(n>0)
	        {
	        	System.out.print((n/Integer.parseInt(s))*Integer.parseInt(s)+" ");
	        	n=n-((n/Integer.parseInt(s))*Integer.parseInt(s));
	        	s=s.substring(0,String.valueOf(n).length());
	        }
	        System.out.println();
		t--;
		}
	}
}