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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

/**
 * <a href="http://codeforces.com/contest/640/problem/A">640A</a>
 */
public class _640A {
    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(reader.readLine());
        for (int w = 0; w < t; w++) {
            int n = Integer.parseInt(reader.readLine());
            if (isRound(n)) {
                System.out.println(1);
                System.out.println(n);
                continue;
            }

            List<Integer> list = new ArrayList<>();
            int length = ("" + n).length();
            for (int i = 0; i < length; i++) {
                int pow = (int) Math.pow(10, length - i - 1);
                int q = n / pow;
                int e = q * pow;
                if (e != 0) {
                    list.add(e);
                }
                n = n % pow;
            }
            System.out.println(list.size());
            System.out.println(list.stream().filter(i -> i > 0).map(Object::toString).collect(Collectors.joining(" ")));

        }
    }

    private static boolean isRound(int n) {
        String s = "" + n;
        return IntStream.range(1, s.length())
                .noneMatch(i -> s.charAt(i) != '0');
    }
}