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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	BufferedReader rd= new  BufferedReader(new InputStreamReader(System.in));
	int t=Integer.parseInt(rd.readLine());
	while(t-- >0)
	{ 
	              int n=Integer.parseInt(rd.readLine());
	              List<Integer> list = new ArrayList<>();
	              int v=n;
	              int c=0;
	              int s=0;
	              while(v!=0){
	                int d= v %10;
	                
	     
	                if(d!=0){
	                     s++;            
	                   list.add((int) (d * Math.pow(10,c)));
	                      
	                }
	                  v=v/10; 
	                      c++;
	              }
	System.out.println(s);
	for(int e :list)
	System.out.print(e +" ");
	System.out.println();
	}
	
	}
}