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);
    Stack<Integer> s = new Stack<>();
    int t = in.nextInt();

    while(t-- > 0) {
      int sum = in.nextInt();
      int n = sum;
      int divider = 10;
      int currentSum = 0;

      while(sum != currentSum) {
        int d = n % divider;
        if (d > 0) {
          s.push(d);
        }
        n -= d;
        currentSum += d;
        divider *= 10;
      }

      System.out.println(s.size());
      while(!s.isEmpty()) {
        System.out.print(s.pop() + " ");
      }
      System.out.println();

    }

  }
}