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 SumofRoundNumbers {

    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        int t = scan.nextInt();
        while (t-- > 0) {
            String s = scan.next();
            ArrayList<Integer> a = new ArrayList<Integer>();
            for (int i = 0; i < s.length(); i++) {
                if (s.charAt(i) != '0') {
                    String e = "";
                    for (int j = 0; j < s.length() - i-1; j++) {
                        e += '0';
                    }
                    e = (s.charAt(i) - '0') + e;
                    int k = Integer.valueOf(e);
                    a.add(k);
                }
            }
            System.out.println(a.size());
            for (int i = 0; i < a.size(); i++) {
                System.out.print(a.get(i)+" ");
            }
            System.out.println();

        }
    }

}