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:
//package codeforces;

import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.Math.*;

import java.io.*;
import java.math.*;
import java.nio.*;
import java.nio.file.*;
import java.time.*;
import java.time.format.*;
import java.time.temporal.*;
import java.util.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;

public class SumOfRoundNumbers {

	public static void main(String[] args) throws Throwable {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		int[] pows = {10_000, 1_000, 100, 10, 1};
		for(int testCase = 1; testCase <= t; testCase++) {
			List<String> terms = new ArrayList<>();
			int num = Integer.parseInt(br.readLine());
			for(int pow : pows) {
				if(pow > num)
					continue;
				final int term = num / pow * pow;
				terms.add(String.valueOf(term));
				num -= term;
			}
			System.out.println(terms.size());
			System.out.println(terms.stream().collect(Collectors.joining(" ")));
		}
	}

	SumOfRoundNumbers() throws Throwable {

	}

}