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.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int num = in.nextInt(), temp;
        List<Integer> list = new ArrayList<Integer>();
        List<Integer> out = new ArrayList<Integer>();
        for (int i=0;i<num; i++){
            temp = in.nextInt();
            for (int j=0; j<Integer.toString(temp).length(); j++){
                list.add(Integer.parseInt(Integer.toString(temp).substring(j,j+1)));
                if(list.get(j)!=0){
                    out.add((int)(list.get(j)*Math.pow(10,Integer.toString(temp).length()-j-1)));
                }
            }
            System.out.println(out.size());
            for(int j=0; j<out.size(); j++){
                System.out.println(out.get(j));
            }
            list.clear();
            out.clear();
        }

    }
}