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.lang.*;
import java.util.*;
import java.util.Collections;
import java.util.LinkedHashSet;
public class Main 
{
  public static void main(String[] args)
  {
    
    
    Scanner ab=new Scanner(System.in);
int te=ab.nextInt();
while(te-->0)
{
	int x=ab.nextInt();
	String str=x+"";
	int n=str.length();int mod=10;
	if(x==0){System.out.println(0);
	continue;
	}
	if(x<=10){System.out.println(1+"\n"+x);}
	else
	{
		int temp=n;
		int arr[]=new int[n];
	int cnt=0;
	 while(n-->0)
	 {
		arr[cnt]=x%mod;
 
		x-=arr[cnt];
		cnt++;
		mod*=10;
 
	 }
	int cn=0;
	for(int i=0;i<arr.length;i++)
	{if(arr[i]!=0)cn++;}  
	System.out.println(cn);
	for(int i=0;i<cnt;i++)
	{if(arr[i]!=0)System.out.print(arr[i]+" ");}
	System.out.println();
	
	}
 
}
 
 
    
    
    
  }
 
}