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 sumofroundnumbers{
    public static void main(String args[]){
        Scanner ob=new Scanner(System.in);
        int n=0,e,c;
        int k=ob.nextInt();
        for(int i=0;i<k;i++){
            n=ob.nextInt();
            c=n;
            e=1;
            int d=0;
            int count=0;
            String str=""+c;
            for (int j = 0; j < str.length(); j++) {
                if (str.charAt(j) != '0') {
                    count++;
                }
            }
            System.out.println(count);
            while(c!=0){
                d=c%10;
                if(d!=0){
                    System.out.print((d*e)+" ");
                }
                e=e*10;
                c=c/10;
            }
            System.out.println();
        }
        ob.close();
    }
}