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.util.*;

public class Solution
{
    public static void main(String ar[])
    {
        int t, n, count, digits, k, j;
        Scanner s = new Scanner(System.in);
        t = s.nextInt();
        for(int i = 0; i < t; i++)
        {
            count = 0;
            digits = 0;
            n = s.nextInt();
            int temp = n;
            while(temp > 0)
            {
                digits++;
                temp /= 10;
            }
            ArrayList <Integer> list = new ArrayList <Integer> ();
            if(n % (Math.pow(10, digits - 1)) == 0)
            {
                count = 1;
                list.add(n);
            }
            else
            {
                k = 0;
                while(n > 0)
                {
                    temp = (n % 10) * (int)(Math.pow(10, k));
                    if(temp != 0)
                    {
                        list.add(temp);
                        count++;
                    }
                    n = (n - temp / (int)(Math.pow(10, k))) / 10;
                    k++;
                }
            }
            System.out.println(count);
            for(Integer num : list)
            {
                System.out.print(num + " ");
            }
            System.out.println();
        }
    }
}