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.List;
import java.util.Scanner;
import java.util.Vector;


public class RoundNumsSum {
    public static void printBinaryString(int number){
        List<Integer> binaryString = new Vector<Integer>();
        int len = Integer.valueOf(number).toString().length() - 1;
        int count = 0;
        while (true){
            int d = number % (int)Math.pow(10, len);
            if (d == 0){
                ++count;
                binaryString.add(number);
                // System.out.print(number + " ");
                break;
            } else if (d % 10 == d) {
                count += 2;
                binaryString.add(number-d);
                binaryString.add(d);
                // System.out.print(number-d + " " + d);
                break;
            } else {
                ++count;
                binaryString.add(number-d);
                // System.out.print((number-d) + " ");
                number -= (number-d);
                len = (Integer.valueOf(number)).toString().length() - 1;
            }
        }
        System.out.println(count);
        for (int bs: binaryString) System.out.print(bs + " ");
        System.out.println();

    }

    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int test = scan.nextInt();
        scan.nextLine();
        while (test >= 1){
            printBinaryString(scan.nextInt());
            --test;
        }
    }
}