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:
/**
 * CodeForces
 * 02/12/2020
 */

import java.util.*;

public class A1352_0640_Sum {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();

        ArrayList<Integer> dig = new ArrayList<Integer>();
        for (int i = 0; i < t; i++) {
            char[] n = scanner.next().toCharArray();
            for (int j = n.length - 1; j >= 0; j--) {

                int digit = Integer.parseInt(String.valueOf(n[j]));
                int x = (int)(Math.pow(10, n.length - j - 1)) * digit;
                if (x != 0) dig.add(x);
            }
            System.out.println(dig.size());
            for (int j = 0; j < dig.size(); j++) {
                System.out.print(dig.get(j));
                System.out.print(" ");
            }
            System.out.println();
            dig.clear();
        }
    }
}