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.Arrays;
import java.util.Scanner;

public class a {
    public static void main(String[] args) {
        Scanner input=new Scanner(System.in);

            int n=input.nextInt();
            int a[]=new int[n];
            for (int i = 0; i <n ; i++) {
                a[i]=input.nextInt();
            }
            for (int i = 0; i <n ; i++) {
                int temp=a[i];
//                if (temp%10==0){
//                    System.out.println(1);
//                    System.out.println(temp);
//                    continue;
//                }
                int k;
                int length;




                ArrayList<Integer> arr=new ArrayList<>();
                while (true){
                     k=10;
                    length=1;
                    int x=temp;
                    while (x/k!=0){
                        x=x/k;
                        length++;
                    }
                    length=length-1;
                    if (length==0){
                        if (temp==0){
                            break;
                        }
                        arr.add(temp);
                        break;
                    }

                    k= (int) Math.pow(10,length);
                    int xx=temp/k;
                    xx=xx*k;
                    arr.add(xx);
                    temp=temp-xx;


                }
                System.out.println(arr.size());
                for (int j = 0; j <arr.size() ; j++) {
                    System.out.print(arr.get(j)+" ");

                }
                System.out.println();


            }

        }

}