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.lang.Math; 

public class Contest {
	public static void main(String[] args){
		
		Scanner input=new Scanner(System.in);
		
		int t=input.nextInt();
		while (t!=0) {
			int a=input.nextInt();
			int i=0;
			ArrayList<Integer> nums = new ArrayList<Integer>();
			while (a!=0) {
				if (a%10!=0) {
					nums.add((((a%10)*((int)(Math.pow(10,i))))));
				}
				i++;
				a=a/10;
			}
			System.out.println(nums.size());
	        for (int m = 0; m< nums.size(); m++)  {
	            System.out.print(nums.get(m) + " ");    
	    } 
	        System.out.println();
			t--;
		}
	}

}