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.*;
public class round
{
	public static void main(String[] args) {
		int i,j,n,cou=0,x=0,d=1,rem=0,b=0;
		Scanner sc= new Scanner(System.in);
		int t = sc.nextInt();
		for(j=0;j<t;j++)
		{
          n=sc.nextInt();
          x=n;
          while(x!=0)
          { rem= x%10;
          	d=d*10+rem;
          	x =x/10;
          	cou++;
          }
          check(d,cou);
          total(d,cou);
          d=1;cou=0;
      }
  }
          public static void total(int d,int cou )
          { int rem =0,i;
          	while(d!=1)
          {
          	rem=d%10;
          	if(rem!=0)
          	{
          	for(i=1;i<cou;i++)
          	{   
          		rem= rem*10;
          	}
          	System.out.println(rem);}
          	rem=0;cou--;
          	d=d/10;
          }
          d=1;
          }
           public static void check (int d,int cou )
          { int rem=0,b=0;
          	while(d!=1)
          {
          	rem=d%10;
          	if(rem!=0)
          	{b++;
          	for(int i=1;i<cou;i++)
          	{   
          		rem= rem*10;
          	}
          	}
          	rem=0;cou--;
          	d=d/10;
          }
          
          
		System.out.println(b);d=1;cou=0;}
	}