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.*;
import java.lang.*;
import java.io.*;
import java.lang.Math;
public class HelloWorld{

     public static void main(String []args){
         Scanner sc = new Scanner(System.in); 
        int t = sc.nextInt();
        while(t-->0){
            int a[]= new int[1000];
            int n= sc.nextInt();
            int c=0,k=0,d=n;
            while(d>0){
                d=d/10;
                c=c+1;
            }
            
            for(int i=0;i<c;i++){
                if(n%10!=0){
                    double p= Math.pow(10,i);
                    int m= (int)p;
                    a[i]=(n%10) *m;
                    k=k+1;
                    n=n/10;
                }
                
                else if(n/10==0){
                    a[i]=(n*(int)(Math.pow(10,i)));
                    k=k+1;
                }
                else{
                    n=n/10;
                    continue;
                }
                
            }
            
                System.out.println(k);
                for(int i = 0; i<c; i++) {
                    if(a[i]!=0){
  System.out.print(a[i] + " ");}
}
            System.out.println("");
                
        }
        

     }
}