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;

/**
 *
 * @author Arles
 */
public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int cases = Integer.parseInt(sc.nextLine());

        while (cases > 0) {
            String number = sc.nextLine();
            if (number.length() == 1) {
                System.out.println("1");
                System.out.println(number);
            } else {
                String output = "";
                int cont = 0;
                //output += number.charAt(0) + " ";
                for (int i = 0; i < number.length(); i++) {
                    if (number.charAt(i) != '0') {
                        output += number.charAt(i);
                        cont++;
                        for (int j = i + 1; j < number.length(); j++) {
                            output += "0";
                        }
                        output += " ";
                    }
                }
                System.out.println(cont);
                System.out.println(output);
            }

            cases--;
        }

    }
}