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.*;

public class D1 {
    public static void main(String args[]) throws IOException{
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t = sc.nextInt();
        while(t--!=0){
            int n = sc.nextInt();
            int m= n;
            int ans=0;
            int y =1;
            ArrayList<Integer> a = new ArrayList<>();
            while(n!=0){
                int x = n%10;
                if(x!=0){
                    ans++;
                    a.add(x*y);
                }
                y *=10;
                n=n/10;
            }
            pw.println(ans);
            for(int i:a){
                pw.print(i+" ");
            }
            pw.println();
        }
        pw.close();
    }
    public static int gcd(int a,int b){
        int ans=1;
        for(int i = 1; i <= a && i <= a; i++)
        {
            if(a%i==0 && b%i==0)
                ans = i;
        }
        return ans;
    }
    static class Scanner {
	StringTokenizer st;
	BufferedReader br;
        
	public Scanner(InputStream s) {
		br = new BufferedReader(new InputStreamReader(s));
	}
        
	public Scanner(String file) throws FileNotFoundException {
		br = new BufferedReader(new FileReader(file));
        }
	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	public String nextLine() throws IOException {
		return br.readLine();
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public boolean ready() throws IOException {
		return br.ready();
	}

    }
}