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.Scanner;




public class test {
/*
    public static int grade (int s){
        if(s.length()>10)
            s=s.charAt(0)+Integer.toString(s.length()-2)+s.charAt(s.length()-1);
        return s;
        }
*/
    public static void main(String[] args) {
        Scanner myObj = new Scanner(System.in);
        
        int input=0,n= myObj.nextInt(),k=0,i=0;
        String x="";
        myObj.nextLine();
        
        while(n>0)
        {
            n--;
            input=myObj.nextInt();
            
            for(i=1,x="",k=0;input>0;input/=10,i*=10)
                if(input%10 != 0)
                {
                    x=x+Integer.toString((input%10)*i)+" ";
                    k++;
                }
            myObj.nextLine();
            System.out.println(k);
            System.out.println(x);
        }
        myObj.close();    
    }    
}