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.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.* ;
import java.io.* ;
@SuppressWarnings("unused")

//Scanner s = new Scanner(new File("input.txt"));
//s.close();
//PrintWriter writer = new PrintWriter("output.txt");
//writer.close();
//BufferedReader in = new BufferedReader(new InputStreamReader(System.in)) ;

//Scanner in = new Scanner(System.in) ;
//[a-z] = [97-122] ------- [A-Z] = [65-90]

public class cf
{	
	static final int mod = 1000000007 ;
	
	static boolean not_prime[] = new boolean[1000001] ;
	static void sieve() {
		for(int i=2 ; i*i<1000001 ; i++) {
			if(not_prime[i]==false) {
				for(int j=2*i ; j<1000001 ; j+=i) {
					not_prime[j]=true ;
				}
			}
		}not_prime[0]=true ; not_prime[1]=true ;
	}	
	
	public static long bexp(long base , long power)
	{
		long res=1L ;
		
		//base = base%mod ;
		
		while(power>0) {
			if((power&1)==1) {
				res=(res*base);//%mod ;
				power-- ;
			}
			else {
				base=(base*base);//%mod ;
				power>>=1 ;
			}
		}
		
		return res ;
	}

	static long modInverse(long n, long p)
	{
	    return power(n, p - 2, p);
	}
	static long power(long x, long y, long p)
	{
	  
	    // Initialize result
	    long res = 1;
	  
	    // Update x if it is more than or
	    // equal to p
	    x = x % p;
	  
	    while (y > 0) {
	  
	        // If y is odd, multiply x
	        // with result
	        if (y % 2 == 1)
	            res = (res * x) % p;
	  
	        // y must be even now
	        y = y >> 1; // y = y/2
	        x = (x * x) % p;
	    }
	  
	    return res;
	}
	static long nCrModPFermat(int n, int r, long p)
	{
		if(n<r) return 0 ;
	    if (r == 0)
	        return 1;

	    long[] fac = new long[n + 1];
	    fac[0] = 1;
	  
	    for (int i = 1; i <= n; i++)
	        fac[i] = fac[i - 1] * i % p;
	  
	    return (fac[n] * modInverse(fac[r], p) % p
	            * modInverse(fac[n - r], p) % p)
	        % p;
	}
	
	private static long modular_add(long a, long b)
	{
	    return ((a % mod) + (b % mod)) % mod;
	}
	private static long modular_sub(long a, long b)
	{
	    return ((a % mod) - (b % mod) + mod) % mod;
	}
	private static long modular_mult(long a, long b)
	{
	    return ((a % mod) * (b % mod)) % mod;
	}
	
	static long lcm(int a, int b)
	{
		return (a / gcd(a, b)) * b;
	}
	private static long gcd(long a, long b)
	{
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	
    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;
        }
    }
	
	//static HashMap<Integer , ArrayList<Integer>> map = new HashMap<>() ;
	static boolean vis[] ;
	public static void main(String[] args)throws IOException//throws FileNotFoundException
    {
	   	FastReader in = new FastReader() ;	
    	StringBuilder op = new StringBuilder() ;
    	int t = in.nextInt() ;
    	while(t-->0)
    	{
    		StringBuilder out = new StringBuilder() ;
    		int n = in.nextInt() ;
    		int d=0, rev=0 , c=0 ;

    		for(int i=n ; i>0 ; )
    		{
    			d++ ;
    			rev=(rev*10)+(i%10) ;
    			if(i%10!=0)c++ ;
    			i/=10 ;
    		}
    		op.append(c+"\n") ; 
    		for(int i=rev ; i>0 ; )
    		{
    			int r = i%10 ; 
    			if(r!=0) 
    			op.append(((int)(r*Math.pow(10,d-1)))+" ") ;
    			i/=10 ;
    			d-- ;
    		}
    		op.append("\n") ;
    	}
    	System.out.println(op.toString());
    }
}