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.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;

public class Contest1 {

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int tc = Integer.parseInt(s.nextLine());

        for (int i = 0; i < tc; ++i) {
            String c = s.nextLine();
            int val = Integer.parseInt(c);
            test(val);
        }
    }

    private static void test(int val) {
        List<Integer> sums = new ArrayList<>();
        int m = 0;
        while (val != 0) {
            int d = val - (val / 10) * 10;
            if (d != 0) {
                sums.add((int) (Math.pow(10, m) * d));
            }

            val /= 10;
            ++m;
        }

        System.out.println(sums.size());
        String collect = sums.stream().map(i -> "" + i).collect(Collectors.joining(" "));
        System.out.println(collect);
    }

}