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 Contest640A
{
	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() { // reads in the next int
			return Integer.parseInt(next());
		}
		public long nextLong() { // reads in the next long
			return Long.parseLong(next());
		}
		public double nextDouble() { // reads in the next double
			return Double.parseDouble(next());
			}
		}
	static InputReader r = new InputReader(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
	public static void main(String[] args)
	{
		int t = r.nextInt();
		for (int i = 0; i < t; i ++)
		{
			String n = r.next();
			int hi = 0;
			for (int j = 0; j < n.length(); j ++)
			{
				if (!(n.charAt(j) == '0'))
				{
					hi ++;
				}
			}
			pw.println(hi);
			for (int j = 0; j < n.length(); j ++)
			{
				if (!(n.charAt(j) == '0'))
				{
					pw.println((int) Integer.parseInt(String.valueOf(n.charAt(j)))* (int) Math.pow(10, n.length() - j - 1));
					
				}
			}
		}
		
		pw.close();
	}
}