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.List;
import java.util.Scanner;

/**
 * Created by rkarumuru on 5/9/20
 **/
public class RoundNumbers {

  private static Scanner scanner = new Scanner(System.in);

  public static void main(String[] args) {

    int t = getInt();
    for (int i = 0; i < t; i++) {
      solve();
    }
  }

  private static void solve() {
    int n = getInt();
    List<Integer> rems = new ArrayList<>();
    while (n > 0) {
      rems.add(n%10);
      n = n/10;
    }
    int exp = 1;
    List<String> soln = new ArrayList<>();
    for (int i = 0; i < rems.size(); i++) {
      if (rems.get(i) != 0) {
        soln.add(exp*rems.get(i) + "");
      }
      exp = exp * 10;
    }
    System.out.println(soln.size());
    System.out.println(String.join(" ", soln));
  }

  public static int getInt() {
    return Integer.parseInt(scanner.nextLine());
  }

  public static String getString() {
    return scanner.nextLine().trim();
  }

  public static double getDouble() {
    return Double.parseDouble(scanner.nextLine());
  }

  public static long getlong() {
    return Long.parseLong(scanner.nextLine());
  }
}