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.*;
import java.io.*;
import java.text.*;
import java.math.*;
import static java.lang.System.*;
import static java.lang.Integer.*;
import static java.lang.Double.*;
import static java.lang.Math.*;

public class Round640_A {
	public void run() throws Exception {
		BufferedReader file = new BufferedReader(new InputStreamReader(System.in));
		
		int cases = Integer.parseInt(file.readLine());
		for(int i = 0; i < cases; i++) {
			int num = Integer.parseInt(file.readLine());
			String out = "";
			int d = 0;
			int count = 0;
			while(num > 0) {
				int curr = num % 10;
				if(curr != 0) {
					out += (int)Math.pow(10,d) * curr + " ";
					count++;
				}
				d++;
				num/= 10;
			}
			System.out.println(count);
			System.out.println(out.trim());
		}
		

		file.close();
	}

	public static void main(String[] args) throws Exception {
		new Round640_A().run();
	}

}