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 final class Solution {
  public static void main(String[] args) {
    Scanner scan = new Scanner(System.in);
    int t = scan.nextInt();
    while(t-->0){
      int count =0;
      int num = scan.nextInt();
      if(num<11){
        System.out.println(++count);
        System.out.println(num);
      } else {
        int dnum = num;
        while(dnum>0){
          int digit = dnum%10;
          dnum /=10;
          if(digit!=0) count++; 
        }
        System.out.println(count);
        int pos = 0;
        while(num>0){
          int dig = num%10;
          num /= 10;
          if(dig==0) {
            pos++;
            continue;
          } else{
            System.out.print(dig*(int)Math.pow(10,pos++)+" ");
          }
          
        }
      }
    }
    scan.close();
    System.out.println();
  }
}