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.ArrayList;
import java.util.Scanner;

public class TaskA {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int res = -10000;
        for (int i = 0; i < n; i++) {
            int a = scanner.nextInt();
            if (a < 10 || (int) ((Math.log(a) / Math.log(10))) == (Math.log(a) / Math.log(10))) {
                System.out.println(1);
                System.out.println(a);
            } else {
                String aString = String.valueOf(a);
                int l = aString.length();
                ArrayList<Integer> list = new ArrayList<>();
                int count = 1;
                while (a > 10) {
                    int m = (int) (Math.pow(10, l - 1));

                    int mult = m * (a / m);
                    a = a - mult;
                    l = String.valueOf(a).length();
                    list.add(mult);


                }
                if (a > 0) {
                    list.add(a);
                }
                System.out.println(list.size());
                for (int ll : list) {
                    System.out.print(ll + " ");
                }
                System.out.println();
            }
        }
    }
}