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 A
{
   public static void main(String[] args) throws IOException
   {
      Scanner sc = new Scanner(System.in);
      int t = Integer.parseInt(sc.nextLine());
      for(int tt = 0; tt < t; tt++){
         String n = sc.nextLine();
         int num = Integer.parseInt(n);
         int sum = 0;
         for(int i = 0; i < n.length(); i++){
            if(n.charAt(i) != '0'){
               sum++;
            }
         }  
         System.out.println(sum);
         for(int i = n.length()-1; i >= 0; i--){
            int rem = num % (int)(Math.pow(10, i));
            if(num - rem != 0){
               System.out.print(num-rem + " ");
            }
            num = rem;
         }
         System.out.println();
      }
   }
}