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.ArrayList;
import java.util.Scanner;
import java.util.Vector;

public class Solution {

    static int n , t ;
    static int [] arr = new int[51];
    static int [] dp  = new int[251];

    public static void main(String[] args) {

       Scanner in = new Scanner (System.in);
       t=in.nextInt();

       for(int j=0;j<t;j++){
           n = in.nextInt();

           int zeros =0,sol=0;
           Vector<Integer> soll = new Vector<Integer>();
           while(n!=0){
               int temp = n%10;
               if(temp==0) {zeros++;n/=10;continue;}
               sol++;
               for(int i=0;i<zeros;i++)
                   temp*=10;
               soll.add(temp);
               n/=10;
               zeros++;
           }
           System.out.println(sol);
           for(int s=0;s<soll.size();s++)
               System.out.print(soll.get(s)+" ");
           System.out.println();
       }

    }
}