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.Scanner;

public class Main
{
	public static void main(String[] args) {
	    Scanner scan = new Scanner(System.in);
	    int n = scan.nextInt();
	    for(int i=0; i<n; i++){
	        int a = scan.nextInt();
	        int[] b;
	        b=solve(a);
	        System.out.println(b[0]);
	        for(int j=b[0]; j>0; j--){
	            System.out.print(b[j]+" ");      
	        }
	        System.out.println();
	    }
	}
	static int[] solve(int n){
	    int[] b = new int[5];
	    int count=0;
	    int ans=1;
	    while(n!=0){
	        if(n%10 != 0){
	            b[count+1] = n%10 * ans;
	            count++;
	        }
	        n/=10;
	        ans *=10;
	    }
	    b[0] = count;
	    return b;
	}
}