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:

//1352A
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Sum_of_Round_Numbers {
    public static void main(String[] args) throws IOException {
        BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
        String test_NumS=bf.readLine();
        int test_Num=Integer.parseInt(test_NumS);
        while(test_Num>0){
            String numS=bf.readLine();
            char numC[]=numS.toCharArray();
            int num[]=new int[numC.length];
            int all=0;
            for (int i = 0; i <numC.length ; i++) {
                int temp=numC[i]-'0';
                num[i]= (int) (temp*Math.pow(10,numC.length-i-1));
                if (num[i]!=0)
                    all++;
            }
            System.out.println(all);
            for (int i = 0; i <num.length ; i++) {
                if (num[i]!=0)
                    System.out.print(num[i]+" ");
            }





            test_Num--;
        }
    }
}