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 src;

import java.util.Scanner;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.StringBuilder;
import java.math.BigInteger;

public class idk {
	static Scanner scn = new Scanner(System.in);

	public static void main(String[] args) {
		
			int t=scn.nextInt();
			while(t-->0)
			{
				String str=scn.next();
				int n=str.length();
				boolean bl=true;
				for(int i=1;i<n;i++)
				{
					if(str.charAt(i)!='0')
					{
						bl=false;
						break;
					}
				}
				if(bl)
				{	System.out.println("1");
					System.out.println(str);
				}
				else
				{	ArrayList<Integer>list=new ArrayList<Integer>();
					int count=0,no=0,sum=0;
					for(int i=n-1;i>0;i--)
					{
						if(str.charAt(i)!='0')
						{
							no++;
							int ans=(int) Math.pow(10, n-i-1)*(str.charAt(i)-48);
							sum+=ans;
							list.add(ans);
						}
					}
					System.out.println(list.size()+1);
					int a=Integer.parseInt(str);
					System.out.print(a-sum+" ");
					for(int i=0;i<list.size();i++)
						System.out.print(list.get(i)+" ");
					System.out.println();
					
				}
				
						
			}
		
	}

	public static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	public static String factorial(int n) {
		BigInteger fac = new BigInteger("1");
		for (int i = 1; i <= n; i++) {
			fac = fac.multiply(BigInteger.valueOf(i));
		}
		return fac.toString();
	}

}