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.util.*;
import java.lang.*;
public class Codechef {
	PrintWriter out;
    StringTokenizer st;
    BufferedReader br;
 	
 	class Pair implements Comparable<Pair>
	{
	    int f;
	    int s;
 
	    Pair(int t, int r) {
	       f = t;
	       s = r;
	    }
	    public int compareTo(Pair p)
	    {
	    	if(this.f!=p.f)
	    		return this.f-p.f;
 
	    	return this.s-p.s;
	    }
 	}
 // 	class Sort implements Comparator<String> 
	// { 
	//     public int compare(String a, String b) 
	//     { 
	//     	return (a+b).compareTo(b+a);
	//     } 
	// }
 
	String ns() {
        while (st == null || !st.hasMoreElements()) {
 
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    String nextLine() throws Exception {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            throw new Exception(e.toString());
        }
        return str;
    }
 
    int nextInt() {
        return Integer.parseInt(ns());
    }
 
    long nextLong() {
        return Long.parseLong(ns());
    }
 
    double nextDouble() {
        return Double.parseDouble(ns());
    }
	
	int upperBound(long a[],int key)
	{
		int l=0,r=a.length-1;
		int i=-1;

		while(l<=r)
		{
			int mid=(l+r)/2;

			if(a[mid]<=key){
				i=mid;
				l=mid+1;
			}

			else{
				r=mid-1;
			}
		}
		return i;
	}

	long power(long x,long y)
	{
	    long ans=1;
	    
	    while(y!=0)
	    {
	        if(y%2==1) ans=(ans*x)%mod;
	        x=(x*x)%mod;
	        y/=2;
	    }
	    return ans%mod;
	}

	long mod= 1000000007;
	long gcd(long x ,long y)
	{
		if(y==0)
			return x;
		return gcd(y,x%y);
	}

	void solve() throws IOException{
		int t=nextInt();
		while(t-->0)
		{
			int n=nextInt();
			ArrayList<Integer> list = new ArrayList<>();
			for(int i=0;n!=0;i++)
			{		
				int r=n%10;
				if(r!=0)
					list.add(r*(int)Math.pow(10,i));
				n/=10;
			}
			out.println(list.size());

			for(int i=0;i<list.size();i++)
				out.print(list.get(i)+" ");
			out.println();

		}
		
	}
  
    void run() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
		solve();
		out.flush();

		out.close();
	}
 
	public static void main(String args[]) throws IOException {
		new Codechef().run();
	}
  
}