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 SumOfRoundNumbers {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int t = sc.nextInt();

        for (int i = 0; i < t; i++) {
            int n = sc.nextInt();
            int noOfUniqueDigits = 0;
            int digitsArray[] = new int[Integer.toString(n).length()];

            for (int j = 0; j < digitsArray.length; j++) {
                int digit = n%10;
                digitsArray[j] = digit;
                n/=10;
            }

            for (int e:digitsArray) {
                if(e>0){
                    noOfUniqueDigits++;
                }
            }
            System.out.println(noOfUniqueDigits);

            for (int j = 0; j < digitsArray.length; j++) {
                String digitString = Integer.toString(digitsArray[j]);
                for (int k = 0; k < j; k++) {
                    digitString += "0";
                }
                digitsArray[j] = Integer.parseInt(digitString);
            }

            for (int j = 0; j < digitsArray.length; j++) {
                if(digitsArray[j]>0) {
                    System.out.print(digitsArray[j]);
                    if (j == digitsArray.length - 1) {
                        System.out.println("");
                    } else {
                        System.out.print(" ");
                    }
                }
            }
        }
    }
}