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.io.*;
	import java.math.*;
	import java.awt.geom.*;
	 
	import static java.lang.Math.*;
	 
	 public class Solution implements Runnable {
		
		 
	    public void solve() throws Exception {
	    	
	    	int t=sc.nextInt();
	    	while(t-->0)
	    	{
	    		int n=sc.nextInt();
	    		int count=0;
	    		int nn=n;
	    		int c=0;
	    		while(nn!=0)
	    		{
	    			if(nn%10!=0)
	    			{
	    				c++;
	    				
	    			}
	    			nn/=10;
	    		}out.println(c);
	    		while(n!=0)
	    		{
	    			if(n%10!=0)
	    			{
	    				
	    				out.print((int)Math.pow(10, count)*(n%10)+" ");
	    			}
	    			n=n/10;
	    			count++;
	    		}
	    		out.println();
	    		
	    		
	    	}
	    }
	    		
	    		
	    		
	    		
	    	
	    
	    		
	    		
	    		
	    		
	   
	    
	   
	    
	    static long power(long x, long y, long p) 
	    { 
	       
	        long res = 1;      
	       
	        x = x % p;  
	  
	       if (x == 0) return 0;    
	  
	        while (y > 0) 
	        { 
	            if((y & 1)==1) 
	                res = (res * x) % p; 
	            y = y >> 1;  
	            x = (x * x) % p;  
	        } 
	        return res; 
	    } 
	    
	    		
	    
	    
	    
	    
	    
	    static Throwable uncaught;
	 
	    BufferedReader in;
	    FastScanner sc;
	    PrintWriter out;
	 
	    @Override
	    public void run() {
	        try {
	            in = new BufferedReader(new InputStreamReader(System.in));
	            out = new PrintWriter(System.out);
	            sc = new FastScanner(in);
	            solve();
	        } catch (Throwable uncaught) {
	            Solution.uncaught = uncaught;
	        } finally {
	            out.close();
	        }
	    }
	 
	    public static void main(String[] args) throws Throwable {
	        Thread thread = new Thread(null, new Solution(), "", (1 << 26));
	        thread.start();
	        thread.join();
	        if (Solution.uncaught != null) {
	            throw Solution.uncaught;
	        }
	    }
	 
	}
	 
	class FastScanner {
	 
	    BufferedReader in;
	    StringTokenizer st;
	 
	    public FastScanner(BufferedReader in) {
	        this.in = in;
	    }
	 
	    public String nextToken() throws Exception {
	        while (st == null || !st.hasMoreTokens()) {
	            st = new StringTokenizer(in.readLine());
	        }
	        return st.nextToken();
	    }
	 
	    public int nextInt() throws Exception {
	        return Integer.parseInt(nextToken());
	    }
	    
	    public int[] readArray(int n) throws Exception {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
	 
	    public long nextLong() throws Exception {
	        return Long.parseLong(nextToken());
	    }
	 
	    public double nextDouble() throws Exception {
	        return Double.parseDouble(nextToken());
	    }
	 
	}