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 P1352A {
    public static void main(String [] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();

        for (int i = 0; i < n; i++) {
            char [] digits = in.next().toCharArray();
            List<Integer> results = new ArrayList<>();

            for (int j = 0; j < digits.length; j++) {
                int number = Character.getNumericValue(digits[j]);
                Double result = number * Math.pow(10, digits.length - j - 1);

                if (result > 0)
                    results.add(result.intValue());
            }

            System.out.println(results.size());
            for (Integer result : results)
                System.out.print(result + " ");
                
            System.out.println();
        }
    }
}