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.io.*;
import java.util.*;

public class Demo1 { 
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder();
        int t =sc.nextInt();
        while(t-->0) {
        	int n = sc.nextInt();
        	if(n<10)
        		sb.append("1\n"+n+"\n");
        	else {
        		String a = Integer.toString(n);
        		int flag = 0;
        		for(int i=0;i<a.length();i++) {
        			if(a.charAt(i)=='0') {	
        				flag++;
        			}
        		}
        		sb.append(a.length()-flag);
        		sb.append("\n");
        		for(int i=0;i<a.length();i++) {
        			if(a.charAt(i)!='0') {
        				String b = "";
        				String zero = "0";
        				String repeated = new String(new char[a.length()-i-1]).replace("\0", zero);
        				b = a.charAt(i)+repeated;
        				sb.append(b+" ");
        			}
        		}
        		sb.append("\n");
        	}
        }
        System.out.print(sb.toString());
        sc.close();
    }
}