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:
/******************************************************************************

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import java.util.*;
import java.io.*;
import java.math.*;

public class Main
{
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int t = s.nextInt();
		while(t--!=0) {
		    String n = s.next();
		    int l = n.length();
		    
		    ArrayList<Integer> arr = new ArrayList<>();
		    int k = 0;
		    for(int i=l-1;i>=0;i--) {
		        if(n.charAt(i) != '0') {
		            arr.add((n.charAt(i) - 48)*((int)Math.pow(10, k)));
		        }
		        k++;
		    }
		    
		    pw.println(arr.size());
		    for(int i=0;i<arr.size();i++){
		        pw.print(arr.get(i) + " ");
		    }pw.println();
		}
		pw.flush();
	}
}