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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.PriorityQueue;


public class Testclass {

    
    public static void main(String[] args) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(br.readLine());
        while(t-->0)
        {
        String n=br.readLine();
        int g=Integer.parseInt(n);
        PriorityQueue<Integer> ar=new PriorityQueue<>();
        while(g>0)
        {
            
            g=Integer.parseInt(n);
            int k=(int)Math.pow(2, n.length()-1);
            String w=Integer.toBinaryString(k);
            int v=Integer.parseInt(w);
            int r=g%v;
            int h=g-r;
            if(h!=0)
            {
            ar.add(h);
            }
            n=Integer.toString(r);
            
        }
           int p=ar.size();
        System.out.println(ar.size());
        for(int i=0;i<p;i++)
        {
            System.out.print(ar.poll()+" ");
        }
            System.out.println(" ");
        }
            
            
        
    }
    
}