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

public class Problem1352a {
	
	private static Scanner sc;

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		sc = new Scanner(System.in);
		
		int t = sc.nextInt();
		
		while(t-- > 0)
		{
			int n = sc.nextInt();
			
			solve(n);
		}
	}
	
	private static void solve(int n)
	{
		int x = 1;
		List<Integer> l = new ArrayList<>();
		
		for(int i = 0; i<=4 ; i++)
		{
			int y = (int) (n% Math.pow(10, x));
			n -= y; 
			if(y != 0)
				l.add(y);
			
			x++;
		}
		
		System.out.println(l.size());
		for(int i : l)	
			System.out.print(i + " ");
		
		System.out.println();
		
	}

}