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.*;


public final class Phoenix
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		while(t-->0)
		{
		    int n=Integer.parseInt(br.readLine());
		    String s=null;
		    s="";
		    int temp=n,count=0,x=0,j=0,cf=0;
		    while(temp!=0)
		    {
		        x=temp%10;
		       // System.out.println("x "+x);
		        j=(int)(x*Math.pow(10,count));
		         // System.out.println("j "+j);
		        if(j!=0)
		        {
		            cf++;
		            s=s+Integer.toString(j)+" ";
		              //System.out.println("s "+s);
		        }
		        count++;
		        temp=temp/10;
		    }
		    System.out.println(cf);
		    System.out.println(s);
		}
	}
}