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 balls{
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		for(int i=0; i<t; i++) {
			int n = sc.nextInt();
			int a = n;
			String s = Integer.toString(n);
			int x = 0;
			for(int k=0; k<s.length(); k++) {
				if(s.charAt(k) != '0'){
					x++;
				}
			}
			System.out.println(x);
			int y = 0;
			for(int j=1; j<=n; j*=10) {
				y = a;
				a = a/10;
				int b = a*10;
				int c = y-b;
				if(c>0) {
					System.out.print(c*j+" ");
				}				
			}			
			System.out.println();
		}
	}
}