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.io.IOException;
import java.util.Scanner;

public class main {



	public static void main(String[] args) throws IOException{



		Scanner obj = new Scanner(System.in);

		long t = obj.nextLong();
		
		for(long i = 0; i < t; i++)
		{
			int count = 0;
			
			Long num = obj.nextLong();
			
			int length = num.toString().length();
			
			String str = "";
			
			if(length == 1)
			{
				System.out.println(1);
				System.out.println(num);
			}
			else
			{
				
				
				for(int x = 0; x < length; x++)
				{
					if(num % 10 != 0)
					{
						str = str + " " + ((int)((num % 10) * Math.pow(10, x)));
						count++;
						
						num /= 10;
					}
					else
						num /= 10;
					
				}
				
				System.out.println(count);
				System.out.println(str);
			
			}
			
		}
	}

}