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 Main {




    static boolean IsRound(String Number)
    {

        for (int i = Number.length()-1; i>=1; i--){

            if(Number.charAt(i)!='0')
            {
                return false;

            }

        }
        return true;






    }



    static void prosess(String Number) {

        if (Number.length() == 1||IsRound(Number)) {
            System.out.println(1);
            System.out.println(Number);
            return;
        }
        ArrayList A = new ArrayList<Integer>();
        for (int i = Number.length()-1; i>=0; i--) {
            if (Number.charAt(i) != '0') {

                    A.add(String.valueOf((int)Math.pow(10,Number.length()-i-1) * Integer.parseInt(String.valueOf(Number.charAt(i)))));

            }


        }
        System.out.println(A.size());

        for(
    int i = 0; i<A.size();i++)

    {


        System.out.print(A.get(i) + " ");


    }

        System.out.println();

}


    public static void main(String[] args) {

        Scanner Input = new Scanner(System.in);
        int length = Input.nextInt();
        for (int i = 0; i < length; i++) {
            prosess(Input.next());


        }


    }


}