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.Scanner;

public class A1352 {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = Integer.parseInt(scanner.nextLine());
        while (t-- > 0) {
            String n = scanner.nextLine();

            int divider = (int) Math.pow(10, n.length() - 1);
            int number = Integer.parseInt(n);
            int count = 0;
            StringBuilder builder = new StringBuilder();
            while (number != 0) {
                int rest = number % divider;
                if (rest != 0) {
                    count++;
                    builder.append(number - rest);
                    builder.append(" ");
                    number = rest;
                    divider = (int) Math.pow(10, ("" + number).length() - 1);
                } else {
                    builder.append(number);
                    count++;
                    break;
                }
            }
            System.out.println(count);
            System.out.println(builder);
        }
    }
}