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.util.ArrayList;
import java.util.List;
import java.util.stream.Collectors;

public class Rounding_the_sum
{
	public static void main (String[] args)
	{
    Scanner sc = new Scanner(System.in);
   int t = sc.nextInt();
   for(int i =0 ;i<t;i++){
       int n = sc.nextInt();
       System.out.println(check(n));
   }
   
   sc.close();
}
static String check(int n){
  List<Integer> terms = new ArrayList<>();
        for (int i = 10000; i >= 1; i /= 10) {
            int term = n / i * i;
            if (term != 0) {
                terms.add(term);
                n -= term;
            }
        }

        return String.format("%d\n%s", terms.size(),
                terms.stream().map(String::valueOf).collect(Collectors.joining(" ")));
    
}
}