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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class q1 {

	public static void main(String[] args) {
		FastReader s = new FastReader();
		
		int t = s.nextInt();
		
		while(t-- > 0)
		{
			int n = s.nextInt();
			ArrayList<Integer> ans = new ArrayList<>();
			int num = 1;
			while(n>0)
			{
				if(n%10 != 0)
					ans.add(0,(n%10)*num);
				num *= 10;
				n = n/10;
			}
			System.out.println(ans.size());
			for(int i =0;i<ans.size();++i)
				System.out.print(ans.get(i) + " ");
			System.out.println();
		}

	}
	private static boolean isDec(int[] nums) {
		for(int i=0;i<nums.length-1;++i)
		{
			if(nums[i] == 1)
			{
				if(nums[i+1] != nums.length)
					return false;
				
			}
			else if(nums[i] != nums[i+1]+1)
				return false;
		}
		
		return true;
	}
	private static boolean isInc(int[] nums) {
		
		for(int i=0;i<nums.length-1;++i)
		{
			if(nums[i] == nums.length)
			{
				if(nums[i+1] != 1)
					return false;
				
			}
			else if(nums[i] != nums[i+1]-1)
				return false;
		}
		
		return true;
	}
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
	}
}