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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Q1352asumofroundnumbers
{
	static String Split(String Number)
	{
		if (Number.length() == 0) return "";
		String Initial = Number.charAt(0) + "";
		for (int i = 1; i < Number.length(); i++) Initial += "0";
		String Current = "";
		for (int i = 1; i < Number.length(); i++)
		{
			if (Number.charAt(i) != '0')
			{
				Current = Split(Number.substring(i, Number.length()));
				break;
			}
		}
		return (Current.equals("")) ? Initial : Initial +  " " + Current;
	}
	
	public static void main(String[] Arguments) throws IOException 
	{
		BufferedReader BR = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(BR.readLine());
		for (; t > 0; t--)
		{
			int n = Integer.parseInt(BR.readLine());
			String S = Split(String.valueOf(n));
			int spaceCount = S.length() - S.replaceAll(" ", "").length();
			System.out.println(spaceCount + 1);
			System.out.println(S);
		}
	}
}