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.lang.*;
public class Main{
    public static void main(String [] args){
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int i =0;i<t;i++){
            ArrayList<Long> a = new ArrayList<>();
            long num = sc.nextLong();
            int c = 0;
            while(num != 0){
                // if(num%10 == 0){
                //     long val = (long)Math.pow(10,Long.toString((long)num).length());
                //     a.add((long)num/val);
                // }
                // else{
                    if(num%10!= 0)
                        c++;
                    a.add(num%10);
                    num = (long)num /10;
                    
                // }           
            }
            System.out.println(c);
            for(int j =a.size()-1;j>=0;j--){
                if(a.get(j) != 0)
                    System.out.print((int)(a.get(j)*Math.pow(10,j))+" ");
            }
            System.out.println("");
        }
    }
}