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 Solution {
    public static void main (String[] args) {
        Scanner sc = new Scanner(System.in);
        
        int t = sc.nextInt();
        
        for (int q=0; q<t; q++) {
            sc.nextLine();
            
            int n = sc.nextInt();
            
            ArrayList<Integer> summands = new ArrayList<Integer>();
            
            int number = n;
            // int noOfDigits = 0;
            
            // while (number > 0) {
            //     number /= 10;
            //     noOfDigits++;
            // }
            
            // number = n;
            int multiplier = 0;
            
            while (number > 0) {
                int msd = number%10;    // Most significant digit
                if(msd > 0) {
                    int summand = msd * (int)Math.pow(10,multiplier);
                    summands.add(summand);
                }
                multiplier++;
                number /= 10;
            }
            
            System.out.println(summands.size());
            
            for(int i=0; i<summands.size()-1; i++) {
                System.out.print(summands.get(i) + " ");
            }
            
            System.out.println(summands.get(summands.size()-1));
        }
    }
}