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 Main{
  public static void main(String[] args)throws IOException{
    BufferedReader br = new BufferedReader (new InputStreamReader (System.in));
    BufferedWriter bw = new BufferedWriter (new OutputStreamWriter (System.out));
    Scanner sc = new Scanner(System.in);
    int test = sc.nextInt();
    int n, temp, len, p = 0, i, count;
    String s,sub,str, print;
    String s1 = "0", s2 = "00", s3 = "000", s4 = "0000";
    for(int t = 0; t < test; t++){
      print = "";
      count = 0;
      n = sc.nextInt();
      s = String.valueOf(n);
      sub = s.substring(1,s.length());
      temp = Character.getNumericValue(s.charAt(0));
      if(n >= 0 && n <=9 || (temp >= 0 && temp <=9 && (sub.equals(s1) || sub.equals(s2) || sub.equals(s3) || sub.equals(s4)))){
        System.out.println("1"+"\n"+n);
      }
      else{
        while(n > 9){
          s = String.valueOf(n);
          len = s.length()-1;
          i = Character.getNumericValue(s.charAt(0));
          int pow = (int)Math.pow(10, len)*i;
          n = n - pow;
          str = String.valueOf(n);
          sub = str.substring(1, str.length());
          i = Character.getNumericValue(str.charAt(0));
          if(n >= 0 && n <=9 || (i >=0 && i <=9 && (sub.equals(s1) || sub.equals(s2) || sub.equals(s3) || sub.equals(s4)))){
            print += pow+" "+n;
            count += 2;
            break;
          }
          else{
            print += pow+" ";
            count += 1;
          }
        }
        System.out.println(count+"\n"+print);
      }
    }
  }
}