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 file{
    public static void main(String[] args){
        Scanner scn = new Scanner(System.in);
        if(scn.hasNext()){
            int t = scn.nextInt();
            for(int xt=0; xt<t; xt++){
                int n = scn.nextInt();
                if(n >= 1 && n <= 9){
                    System.out.println("1");
                    System.out.println(n);
                }else{
                    StringBuilder sb = new StringBuilder("");
                    int k = 0;
                    int pv = 1;
                    while(n != 0){
                        int rem = n%10;
                        n = n/10;
                        if(rem != 0){
                            k++;
                            sb.append(rem*pv + " ");
                        }
                        pv *= 10;
                    }
                    System.out.println(k);
                    System.out.println(sb);
                }
            }
        }
    }
}