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.*;
import java.util.*;
public class SumOfRoundNumbers
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0)
        {
            int n=sc.nextInt();
            int c=0;
            List<Integer> l=new ArrayList();
            String s=String.valueOf(n);
            for(int i=s.length()-1;i>=0;i--)
            {
                if(s.charAt(i)!='0')
                {
                    c++;
                    String h="";
                    h+=s.charAt(i);
                    int e=Integer.parseInt(h);
                    int f=e*(int)Math.pow(10,(s.length()-i-1));
                    l.add(f);
                }
            }
            System.out.println(l.size());
            for(int i=0;i<l.size();i++)
                System.out.print(l.get(i)+" ");
            System.out.println();
        }
    }
}