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 Candies {
static void Sum(long n) {
	String s=""+n;
	int len= s.length();
	System.out.println(rep(n));
	for(int i=0; i<s.length() ; i++) {
//		System.out.println(s.substring(i,i+1)+"in");
		if(s.substring(i,i+1).equals("0")==false) {
		System.out.print(s.charAt(i));
		int p=s.length()-i;
		while(--p>0) {
			System.out.print(0);
			
		}
		System.out.print(" ");
		}
		len--;
	}
	System.out.println();

	
}
static int rep(long n) {
	int rep=0;
	while(n>0) {
//		System.out.println(n%10+" this is");
		if(n%10>0)
		rep++;
		n=n/10;
//		System.out.println(n+" n val");
	}
	return rep;
}
	public static void main(String[] args) {
		Scanner sc= new Scanner(System.in);
		int t= sc.nextInt();
		while(t-->0) {
			long r= sc.nextInt();
			Sum(r);
		}
	}

}