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.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        int counter = scn.nextInt();
        scn.nextLine();
        for (int i = 0; i < counter; i++) {
            String str = scn.nextLine();
            int strlen = str.length();
            StringBuilder strin = new StringBuilder(str);
            StringBuilder strout = new StringBuilder("");
            int mincount = 0;
            for (int j = strlen - 1; j >= 0; j--) {
                if (strin.charAt(j) != '0') {
                    mincount++;
                    strout.append(strin.charAt(j));
                    for (int k = 0; k < strlen - 1 - j; k++) {
                        strout.append("0");
                    }
                    if (j != 0) {
                        strout.append(" ");
                    }
                }
            }
            System.out.println(mincount);
            System.out.println(strout.toString());
        }
    }
}