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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Problem {
    public static void main(String[] args) {
    FastReader sc = new FastReader();
         int t=sc.nextInt();
         while(t-->0)
         {
             int n = sc.nextInt();
          List<Integer> al=new ArrayList<>();
           int mul=10;   
          while(n!=0)
             {
                 int mod=n%mul;
                 if(mod!=0)
                 al.add(mod);
                 n=n-mod;
                 mul=mul*10;
             }
             System.out.println(al.size());
             for(int i=0;i<al.size();i++)
             {
                 System.out.print(al.get(i)+" ");
             }
             System.out.println();
         }
    }
}
class FastReader {    

    BufferedReader br;    
    StringTokenizer st;    
    
    public FastReader() {        
        br = new BufferedReader(new InputStreamReader(System.in));        
    }    
    
    String next() {        
        while (st == null || !st.hasMoreElements()) {            
            try {                
                st = new StringTokenizer(br.readLine());                
            } catch (Exception e) {                
                e.printStackTrace();                
            }            
        }        
        return st.nextToken();        
    }    
    
    int nextInt() {        
        return Integer.parseInt(next());        
    }    
    
    long nextLong() {        
        return Long.parseLong(next());        
    }    
    
    double nextDouble() {        
        return Double.parseDouble(next());        
    }    
    
    String nextLine() {        
        String str = "";        
        try {            
            str = br.readLine();            
        } catch (Exception e) {            
            e.printStackTrace();            
        }        
        return str;        
    }    
}