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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;
 
public class Solution 
{ 
   
 
           
    public static void main(String[] args) throws IOException 
    { 
  
       BufferedReader br = new BufferedReader( 
                              new InputStreamReader(System.in));
        StringBuilder out=new StringBuilder(); 
        int n=Integer.parseInt(br.readLine());
      for(int i=0;i<n;i++){
          String str=br.readLine();
          int addends=0;
          ArrayList<Integer>ans=new ArrayList<>();
          for(int j=0;j<str.length();j++){
              int d=str.charAt(j)-'0';
              if(d!=0){
                  addends++;
                  int num=(int)Math.pow(10,str.length()-j-1)*d;
                  ans.add(num);
              }
          }
          out.append(addends+"\n");
          for(int j=0;j<ans.size();j++)
          out.append(ans.get(j)+" ");
          out.append("\n");
      }
      System.out.println(out);
}}