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 JavaApplication2 
{
    
    public static void main(String[] args) 
    {
        Scanner in = new Scanner(System.in);
        int k=in.nextInt();
        while(k>0)
        {
            String n=in.next();
        int count =1;
        String ans =String.valueOf(n.charAt(0));
        for(int i=1;i<n.length();i++)
        {
            ans+="0";
        }
        for(int i=1;i<n.length();i++)
        {
            char c =n.charAt(i);
            if(c!='0')
            {
                ans+=" "+String.valueOf(n.charAt(i));
                for(int j=i+1;j<n.length();j++)
                    ans+="0";
                count++;
            }
                
        }
        System.out.println(count);
        System.out.println(ans);
        k--;
        }
        
    }
    
    

}