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.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;
import java.util.Stack;
public class Solution {
	
    public static void main(String[] args) {
    	Scanner sc = new Scanner(System.in);
    	int t =sc.nextInt();
    	while(t-->0) {
    		int n=sc.nextInt();
    		int temp = n;
    		ArrayList<Integer> ll = new ArrayList<>();
    		int i=0;
    		while(temp!=0) {
    			if(temp%10!=0) {
    				int tt = (int)Math.pow(10, i);
    				ll.add((temp%10)*tt);
    			}
    			i++;
    			temp =temp/10;
    		}
    		System.out.println(ll.size());
    		for( i=ll.size()-1;i>=0;i--) {
    			System.out.print(ll.get(i)+" ");
    		}
    	}
    	
    	
    }
    }