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 rni {
	static void listprinter(ArrayList gg) {
		System.out.println(gg.size());
		for(int i=0;i<gg.size();i++) {
			System.out.print(gg.get(i)+" ");
			
			
		}
		System.out.println();
		
		
		
	}

	public static void main(String[] args) {
		Scanner in=new Scanner(System.in);
		int t;
		t=in.nextInt();
		int[] p= {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000};
		for(int i=0;i<t;i++) {
			int n=in.nextInt();
			ArrayList<Integer> tt=new ArrayList<>();
			int temp=n;
			while(temp>10) {
				int temp1=temp%10;
				tt.add(temp1);
				temp=temp/10;
				
				
				
				
			}
			tt.add(temp);
			//Collections.reverse(tt);
			//for(int j=0;j<tt.size();j++) {
				//System.out.print(tt.get(j)+" ");
				
			//}
			//System.out.println();
			ArrayList<Integer> fa=new ArrayList<>();
			for(int k=0;k<tt.size();k++) {
				if(tt.get(k)!=0) {
					fa.add(tt.get(k)*p[k]);
					
					
				}
				
				
				
			}
			listprinter(fa);
			
			
			
		}
		// TODO Auto-generated method stub

	}

}