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.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeSet;

public class Main {
    static ArrayList<Long> piramids = new ArrayList<>();
    public static void main(String[]args){
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- != 0) {
            int v = sc.nextInt();
            ArrayList<String> ans = new ArrayList<>();
            int scale = 0;
            while (v > 0)
            {
                int d = v % 10;
                v /= 10;
                if(d != 0) {
                    StringBuilder sb = new StringBuilder();
                    sb.append(d);
                    for(int i = 0; i < scale; i++)
                    {
                        sb.append(0);
                    }
                    ans.add(sb.toString());
                }
                scale++;
            }

            System.out.println(ans.size());
            ans.forEach(x->System.out.print(x + ' ') );
            System.out.println();
        }
    }
}