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.List;
import java.util.ArrayList;
import java.util.Scanner;

public class ROundOff {
	public static void main(String[] args) {

		Scanner s = new Scanner(System.in);

		int t = s.nextInt();

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

			int n = s.nextInt();

			String str = Integer.toString(n);
			List<Integer> list = new ArrayList<Integer>();

			for (int j = 0; j < str.length(); j++) {

				if (str.charAt(j) != '0') {

					int p = (str.length() - 1) - j;

					int ans = (int) ((str.charAt(j) - '0') * Math.pow(10, p));

					list.add(ans);
				}
			}
			System.out.println(list.size());
			
			
			String text = list.toString().replaceAll("(^\\[|\\]$)", "");
			text=text.replaceAll(",","");
			System.out.println(text);

		}

	}

}