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.ArrayList;
import java.util.Scanner;

public class codeforces {
public static void main(String[] args) {
	Scanner scn=new Scanner(System.in);
	int t=scn.nextInt();
	while(t--!=0) {
		int n=scn.nextInt();
		int digit=-1;
		int temp=n;
		while(temp!=0) {
			digit++;
			temp=temp/10;
		}
		int sum=0;
//		int count=0
				ArrayList<Integer>al=new ArrayList<>();
		while(n!=0) {
		  int q=n/(int)Math.pow(10, digit);
		  
		  sum=q*(int)Math.pow(10, digit);
//		  System.out.print(sum+" ");
		  al.add(sum);
		  int rem=n%(int)Math.pow(10, digit);
		  String num=rem+"";
		  n=rem;
		 if(num.length()!=digit) {
			 digit=num.length()-1;
		 }
		 else {
			 digit--;
		 }
		 
		}
		System.out.println(al.size());
		for(int i=0;i<al.size();i++) {
			System.out.print(al.get(i)+" ");
		}
		System.out.println();
	}
}
}