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 Main
{
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		while(t-- > 0){
		    int n = s.nextInt();
		    int count = 0;
		    int addends = 0;
		    String cur = String.valueOf(n);
		    
		    StringBuilder str = new StringBuilder();
		    for(int i = cur.length() - 1; i >=0 ; i--){
		        char cc = cur.charAt(i);
		        if(cc != '0'){
		            addends++;
		            str.append(Integer.parseInt("" + cc));
		          //  System.out.print();
		            int temp = count;
		            while(temp-- > 0){
		                str.append(0);
		              //  System.out.print(0);
		            }
		            str.append(" ");
		        }
		        count++;
		    }
		    
		    System.out.println(addends);
		    System.out.println(str);
		}
	}
}