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.lang.*; 
import java.util.*; 
 
public class Main { 
static String[] arr=new String[2];
public static void main(String[] args){ 
    Scanner in = new Scanner(System.in); 
    int n=in.nextInt(); 
   
    for(int k=0;k<n;k++){
       int x=in.nextInt();
       int div=10;
       int count=0;
       String ans="";
       int temp;
       while(x>0){
           
           temp=x%div;
           x=x-temp;
           div*=10;
            if(temp!=0){
           count++;
           if(count==1)
           ans+=""+temp;
           else
           ans+=" "+temp;
            }
           
       }
       
       System.out.println(count);
       System.out.println(ans);
            
        }
      // String ans=solve();
       
        
    }
   
    
    public static String solve(){
        String ans="";
        
        
        
        
        return ans;
    }
}