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.*;

public class Try
{
	public static void main(String args[])
	{
		Scanner br=new Scanner(System.in);
		int t=br.nextInt();
		while(t>0)
		{
			t--;int n=br.nextInt();int s=0,s1=1;
			int m=n;
			while(n>9)
			{
				if(n%10==0)
				{
					s++;
				}
				s1++;
				n/=10;
			}
			System.out.println(s1-s);
			s=1;
			while(m!=0)
			{
				if(m%10!=0)
				System.out.print((m%10)*s+" ");
				m/=10;
				s*=10;
			}
			System.out.println();
		}
	}
}