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.*;
import java.io.*;

public class sumOfRoundNumbers {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        while(n-->0){
            int counter=0;
            int num = sc.nextInt();
            int ones = num%10;
            int tens = num%100-ones;
            int hundreds = num%1000-tens -ones;
            int thousands = num%10000-hundreds-tens-ones;
            int tenThousands = num%100000-thousands-hundreds-tens-ones;
            StringBuilder yourmom = new StringBuilder();
            if(ones != 0){
                counter=counter+1;
                yourmom.append(ones + " ");
            }
            if(tens != 0){
                counter=counter+1;
                yourmom.append(tens + " ");
            }
            if(hundreds != 0){
                counter=counter+1;
                yourmom.append(hundreds + " ");

            }
            if(thousands != 0){
                counter=counter+1;
                yourmom.append(thousands + " ");

            }
           if(tenThousands != 0){
                counter=counter+1;
                yourmom.append(tenThousands + " ");

            }
            System.out.println(counter);
            System.out.println(yourmom);



        }

    }
}