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.Scanner;

    public class A1352 {

        static int t;
        static Scanner sc = new Scanner(System.in);

        static void moving(int a) {
            ArrayList<Integer> f = new ArrayList<>();
            int i = 1, b;
            while (a != 0) {
                b = (a % 10) * i;
                a /= 10;
                i *= 10;
                if (b == 0) {
                    continue;
                } else {
                    f.add(b);
                }
            }

            System.out.println(f.size());
            for (Integer it : f) {
                System.out.print(it + " ");
            }
            System.out.println("");
            f.clear();
        }

        public static void main(String[] args) {
            t = sc.nextInt();
            for (int j = 0; j < t; j++) {
                int rs = sc.nextInt();
                if (rs <= 9) {
                    System.out.println(1);
                    System.out.println(rs);
                } else {
                    moving(rs);
                }

            }
        }

    }