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.*;
import java.util.Scanner;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef {
	/**
	 * @param args
	 * @throws java.lang.Exception
	 */
	public static void main(String[] args) throws java.lang.Exception {

		Scanner s = new Scanner(System.in);
		int tests = s.nextInt();
	    ArrayList<Integer> solution = new ArrayList<Integer>();

		while (tests > 0) {
			tests--;
			int source=s.nextInt(); 
				int digitsPlace=1;
				int count=0;
				while(source!=0) {
					if(source%10>0) {
						solution.add(source%10*digitsPlace);
					}
					digitsPlace=digitsPlace*10;
					source=source/10;
				}
				
				System.out.println(solution.size());
				for(int k=0;k<solution.size();k++) {
					System.out.print(solution.get(k)+" ");
				}
			solution.clear();
		}

	}
}