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 abc
{
     public static void main(String ar1[])throws IOException
     {
          BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
          int t=Integer.parseInt(br.readLine());
          while(t-->0)
          {
               ArrayList<Integer>ar=new ArrayList<Integer>();
               int n=Integer.parseInt(br.readLine());
               
                    int r=1;
               while(n>10)
               {
               int t1=n%10;
               if(t1!=0)
               ar.add(t1*r);
               n/=10;
               r*=10;
               }
               ar.add(n*r);
               System.out.println(ar.size());
               for(int i:ar)
               System.out.print(i+" ");
               System.out.println();
          
          }
          }
}