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.Scanner;

public class roundOfSum {

    public static void main(String[] args) {
        String input;
        int n;
        Scanner s = new Scanner(System.in);
        n = s.nextInt();
        for (int i =0 ; i < n ; i++){
            input = s.next();
            int len = input.length();
            int [] sumand = new int[len];
            for (int x =0 ; x < len; x++){
                if (input.charAt(x) == '0'){
                    sumand[x] =  -1;
                }else{
                    sumand[x] =  (input.charAt(x) - 48) * (int) Math.pow(10,len-x-1);
                }
            }
            int count = 0;
            for(int value : sumand) {
                if (value != -1) {
                    count++;
                }
            }
            System.out.println(count);
            for (int value : sumand) {
                if (value != -1) System.out.print(value+" ");
            }
            System.out.println();
        }
    }
}