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.*;
public class RoundNumbers{
     public static void main(String[] args){
          Scanner sc =new Scanner(System.in);
          int T =sc.nextInt();
          for(int i =0; i<T; i++){
               int n =sc.nextInt();
               if(n ==10000){
                    System.out.println("1");
                    System.out.println("10000");
                    continue;
               }
               int arr[] = new int[4];
               int ans=0;
               for(int j =3; j>=0; j--){
                    arr[j] = n%10;
                    n= n/10;
                     if(arr[j] != 0){
                          for(int k=1; k<=3-j; k++){
                          arr[j] = arr[j] *10;
                          }ans++;
                     }
               }System.out.println(ans);
               
               for(int j =0; j<4; j++){
                     if(arr[j] != 0){
                         System.out.print(arr[j]+" ");
                     }
               }System.out.println("");
               
               
               
             
              
          }
     }
}