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.LinkedList;
import java.util.Scanner;

public class Main{
        public static void main(String[] args) {
            Scanner sc = new Scanner(System.in);
            int ts = sc.nextInt();
            for(int i=0; i<ts; i++){
                int count = 0;
                int p=1;
                int div = 10;
                LinkedList<Integer> list=new LinkedList<Integer>(); 
                int number = sc.nextInt();
                while(number>0){
                    if(number%div!=0){
                        count+=1;
                        list.add((number%div)*p);
                    }
                    number /=10;
                    p*=10;
                    // div*=10;
                }
                System.out.println(count);
                for(Integer color:list) {
                    System.out.print(color + " ");
                }
                System.out.println(""); 
            }
            sc.close();

        }
        
    }