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.*;
import java.lang.String;
 public class div2{

   public static void main(String[] args){
     Scanner sc = new Scanner(System.in);
      int test = sc.nextInt();
      int ar[] = new int[test];
      for(int i=0;i<test;i++){
        ar[i] = sc.nextInt();
      }
      for(int i=0;i<test;i++){
         if(ar[i]<=10){
           System.out.println(1);
           System.out.println(ar[i]);
         }
         else if(summ(ar[i])){
          System.out.println(1);
          System.out.println(ar[i]);
         }
         else{
           int k = 1;
           ArrayList<Integer> arr = new ArrayList<>();
          while(ar[i]>0){
            if(ar[i]%10 != 0){
              arr.add((ar[i]%10)*k);
            }
            k=k*10;
            ar[i] = ar[i]/10;
          }
          int ss = arr.size();
          System.out.println(ss);
           for(int q = 0;q<ss-1;q++){
             System.out.print(arr.get(q)+" ");
           }
           System.out.println(arr.get(ss-1));
         }
         

        }
        

      }
      static boolean summ(int data){
        int c =0;
        int k = data,le=0;
        while(k>0){
          le++;
          k=k/10;
        }
        while(data>9){
            if(data%10 == 0){
              c++;
            }
            data = data/10;
        }
        if(c == --le)
        return true;
        else
        return false;
      }
      static int first(int data){
        while(data>9){
          data = data/10;
        }
        return data;
      }
  
      }