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.*;
import java.util.ArrayList;

import static java.lang.System.in;
import static java.lang.System.out;
public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(in));
        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(out));
        int t = Integer.parseInt(reader.readLine());
        for (int i = 0; i < t; i++) {
            int n = Integer.parseInt(reader.readLine());
            long res = 1;
            ArrayList<Long> arlist = new ArrayList<>();
            while(n>0){
                int t1 = n%10;
                if(t1!=0) {arlist.add(t1*res);}
                res*=10;
                n=n/10;
            }
            writer.write(arlist.size()+"\n");
            for(long l : arlist) writer.write(l+" ");
            writer.newLine();
        }
        writer.flush();
    }
}