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 Main {
    public static void main(String[] args){

        Scanner kbd = new Scanner(System.in);

        int testcase = kbd.nextInt();

        String input;
        int cnt = 0, curChar, inputInt;

        int arr[] = new int[5];

        boolean flag = true;

        for(int i = 0 ; i < testcase ; i++){

            inputInt = kbd.nextInt();
            input = Integer.toString(inputInt);




            for(int j = input.length(), k = 1, curInt = 0; j > 0; j--, k++){
                curChar = input.charAt(j-1)-'0';

                if( curChar >= 1 && curChar <= 9){
                    arr[cnt]=(int) (curChar * Math.pow(10,k-1));
                    cnt++;


                }



            }
            System.out.println(cnt);
            for(int g = 0; g< cnt; g++){
                System.out.print(arr[g]+" ");
                arr[g] =0;
            }


            cnt =0;


        }

    }





}