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 sumofrounds {
    static int c=0;
    public static void main(String args[]) throws IOException {
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t, i, j;
        t = Integer.parseInt(br.readLine());
        int n[] = new int[t];
        int k[] = new int[t];
        String r[]=new String[t];
        String s;
        String str="";;
        int len;
        for (i = 0; i < t; i++) {
            // StringTokenizer s1 = new StringTokenizer(br.readLine());
            // int len=s1.length();
            s=br.readLine();
            len=s.length();
              n[i] = Integer.parseInt(s);
            r[i]=findsum(n[i],len);
            k[i]=c;


        }
        for(i=0;i<t;i++){
            System.out.println(k[i]+"\n"+r[i]);
        }
    }
    public static String findsum(int n,int l){
       
        String str="";
        int div;
        div=(int)Math.pow(10,l-1);
        c=0;
        
        
        while(l!=1){
            str+=(n-n%div)+" ";
            n=n%div;
            l=Integer.toString(n).length();
            c++;
            div=(int)Math.pow(10,l-1);
        }
        if(l==1 && n!=0){
            str+=n+" ";
            c++;
        }
        
return str;
    }
}