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 in = new Scanner (System.in);
		int n = in.nextInt();
		for (int i = 0;i<n;i++) {
			int a = in.nextInt();
			int b = a;
			int count = 0;
			while (b!=0) {
				if (b%10!=0) {
					count++;
					b/=10;
				}else {
					b/=10;
				}
			}
			System.out.println(count);
			if (a<=10) {
				System.out.println(a);
			}else {
				
				int k = 1;
				boolean flag = false;
				while (a!=0) {
					
					if (!flag) {
						if (a%10==0) {
							a/=10;
							
							flag = true;
						}else {
							count--;
							if (count==0) {
								System.out.print(a%10);
								a/=10;
								continue;
							}
							System.out.print(a%10+" ");
							a/=10;
							flag = true;
						}
					}else {
						int m = a%10;
						if (m==0) {
							k++;
							a/=10;
						}else {
							count--;
							if (count==0) {
								System.out.print(m*(int)Math.pow(10, k));
								a/=10;
								continue;
							}
							System.out.print(m*(int)Math.pow(10, k)+" ");
							k++;
							a/=10;
						}
					}
					
				}
				System.out.println();
			}
		}

	}

}