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 Dij
{

	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int t=in.nextInt();
		while(t-->0)
		{
		   String s=in.next();
		   int count=0;
		   int pow=0;
		   ArrayList<Integer> arr=new ArrayList<>();
		   for(int i=s.length()-1;i>=0;i--)
		   {
			   if(s.charAt(i)!='0')
			   {
				   int x=s.charAt(i)-'0';
				   x=x*(int)Math.pow(10,pow);
				   
				   arr.add(x);
			   }
			   
			   pow++;
		   }
		   System.out.println(arr.size());
		   for(int el:arr)
		   {
			   System.out.print(el+" ");
		   }
			System.out.println();
		}
}
}