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.*;

public class Solution {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int t = Integer.parseInt(br.readLine());
    for (int i=0; i < t; i++) {
      int n = Integer.parseInt(br.readLine());
        solve(n);
      }
    }
  public static void solve(int r) {
    int digits = 0;
    int appends = 0;
    String s = "";
    while(r != 0) {
      String f = Integer.toString(r);
      int len = f.length()-1;
      if(f.charAt(len) != '0') {
        s = s + Integer.toString(Integer.parseInt(String.valueOf(f.charAt(len))) * (int)Math.pow(10, (double)digits));
        s = s + " ";
        appends++;
      }
      digits++;
      r = r/10;
    }
    System.out.println(appends);
    System.out.println(s);
  }
}