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:
/*package whatever //do not write package name here */

import java.util.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc=new Scanner(System.in);
		int t =sc.nextInt();
		while(t-->0){
		    int n=sc.nextInt();
		    int s=n;
		    int i=0;
		    int count=0;
		    long[] arr=new long[n];
		    while(s>0){
		        int k=s%10;
		        long l=(long)(k*Math.pow(10,i));
		        if(k!=0){
		        count++;
		        arr[i]=l;
		            
		        }
		        s/=10;
		        i++;
		    }
		    System.out.println(count);
		    
		    for(int j=0;j<arr.length;j++){
		        if(arr[j]!=0)
		        System.out.print(arr[j]+" ");
		    }
		    System.out.println();
		}
	}
}