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.util.*;

public class Solution{
	private static Scanner in;
	
	public static boolean isRound(int num){
		int count = 1;
		int n = num;
		while(n > 10){
			n = n/10;
			count++;
		}
		
		return n*(int)Math.pow(10, count-1) == num;
	}
	public static void solve(){
		int n = in.nextInt();
		ArrayList<Integer> nums = new ArrayList<Integer>();
		int count = 1;
		while(!isRound(n)){
			
			int x = (int)Math.pow(10, count);
			while(n%x == 0){
				count++;
				x = (int)Math.pow(10, count);
			}
			nums.add(n%x);
			n -= n%x;
			count++;
		}
		nums.add(n);
		System.out.println(nums.size());
		for(int num: nums){
			System.out.print(num+" ");
			
		}
		System.out.println();
	}

	public static void main(String[] args){
		in = new Scanner(System.in);
		int t = in.nextInt();

		for(int i = 0; i < t; i++){
			solve();
		}	
	}
}