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.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class App {
    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        String next() { // reads in the next string
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() { return Integer.parseInt(next()); } // reads in the next int
        public long nextLong() { return Long.parseLong(next()); } // reads in the next long
        public double nextDouble() { return Double.parseDouble(next()); } // reads in the next double
    }
    static InputReader r = new InputReader(System.in);
    static PrintWriter pw = new PrintWriter(System.out);
    public static void main(String[] args) {
        // YOUR CODE HERE
        int length = r.nextInt();
        for(int i=0; i<length; i++){
            int number = r.nextInt();
            ArrayList<Integer> list = new ArrayList<>();

            if(number>=0 && number<=10){
                list.add(number);
                pw.println(list.size());
                for(int j=0; j<list.size(); j++){
                    pw.print(list.get(j) + " ");
                }
                pw.println();
            }
            else{
                int factor = 10;
                while(!isRound(number)){
                    int remainder = number%factor;
                    if(remainder != 0)
                        list.add(remainder);
                    number = number-remainder;
                    factor = factor*10;
                }

                if(isRound(number) && number !=0) list.add(number);

                pw.println(list.size());
                for(int j=0; j<list.size(); j++){
                    pw.print(list.get(j) + " ");
                }
                pw.println();
            }
        }
        pw.close(); // flushes the output once printing is done
    }
    static boolean isRound(int n){
        if(n>=0 && n<=10) return true;
        else{
            String number = n+"";
            ArrayList<String> list = new ArrayList<>(Arrays.asList(number.split("")));
            for(int i=1; i<list.size(); i++){
                if(list.get(i) != "0") return false;
            }
        }
        return true;
    }
}

//125
//1 , 5, 10, 20, 100