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.nio.charset.*;
import java.util.*;
public class TestClass {
    public static void main(String[] args) throws Exception {
        StringBuilder out = new StringBuilder();
        StringTokenizer tk;
        Reader.init(System.in);
       int t = Reader.nextInt();
       while (t-->0){
         String s = Reader.next();
         List<String>arr  = new ArrayList<>();
           for (int i = 0; i <s.length() ; i++) {
               if(s.charAt(i) != '0'){
                   arr.add(s.charAt(i)+get0(s.length()-1-i));
               }
           }
           System.out.println(arr.size());
           for (int i = 0; i <arr.size() ; i++) {
               System.out.print(arr.get(i)+" ");
           }
           System.out.println();
       }
    }
    public static String get0(int n){
        String res = "";
        while (n>0){
            res+=0;
            n--;
        }
        return res;
    }
}

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    static void init(InputStream input) throws UnsupportedEncodingException {
        reader = new BufferedReader(
                new InputStreamReader(input, StandardCharsets.UTF_8));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}