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.*;
public class Main {

    public static void main(String[] args) {
        Scanner s=new Scanner(System.in);
        int t=s.nextInt();
        int inp[]=new int[t];
        for(int i=0;i<t;i++){
            inp[i]=s.nextInt();
        }

        for(int i=0;i<t;i++){
            int num=inp[i];
            int mult=1;
            List<Integer> res=new ArrayList<>();
            while(num>0){
                if(num%10==0){
                    num/=10;
                    mult*=10;
                    continue;
                }
                res.add((num%10)*mult);
                mult*=10;
                num/=10;
            }
            System.out.println(res.size());
            for (int j=0;j<res.size();j++){
                System.out.print(res.get(j)+" ");
                if(j==res.size()-1)
                    System.out.println();
            }
        }
    }
}