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.List;
import java.util.Scanner;

public class ProblemA {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while(t-->0) {
        	int n = in.nextInt();
        	List<Integer> re = new ArrayList<>();
        	double p =0;
        	while(n>0){
        		int d = n%10;
        		if(d!=0){
        			int r = d*(int)(Math.pow(10, p));
        			re.add(r);
        		}
        		p++;
        		n = n/10;
        	}
        	
        	if(n!=0){
        		re.add(n);
        	}
        	System.out.println(re.size());
        	
        	for(int i: re)
        		System.out.print(i +" ");
        	System.out.println("");
        }
	}

}