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 HelloWorld{

     public static void main(String []args){
         Scanner sc = new Scanner(System.in);
         int test = sc.nextInt();
         sc.nextLine();
         while (test>0){
             String s = sc.nextLine();
             String ans = "";
             int count =0;
             String a = ""+s.charAt(0);
             for (int i=1;i<s.length();i++){
                 if (s.charAt(i) =='0'){
                     a+=s.charAt(i);
                 }else{
                     for (int j =0;j<s.length()-i;j++){
                         a+="0";
                     }
                     ans+=a+" ";
                     count++;
                     a=""+s.charAt(i);
                 }
             }
             ans+=a;
             count++;
             System.out.println(count);
             System.out.println(ans);
             test--;
         }
     }
}