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 sum_of_round_numbers {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		
		Scanner in=new Scanner(System.in);
		int t=in.nextInt();
		
		while(t-->0) {
			int n=in.nextInt();
			int tn=1;
			int count=0;
			String s="";
			while(n>0) {
				if(n%10>0) {
				count++;
				s+=(n%10*tn+" ");
				}
				n/=10;
				tn*=10;
				
			}
			System.out.println(count);
			System.out.println(s);
		}
		
		
	/*	for(int i=0;i<t;i++) {
			n[i]=in.nextInt();
		}
		
		for(int i=0;i<t;i++) {
			int ths=0;
			int hds=0;
			int tns=0;
			int ons=1;
	//		n[i]=in.nextInt();
			if(n[i]<10) {
				ons=n[i];
			}
			if(n[i]>10) {
				ths=n[i]/10;
				ths*=10;
				ths=n[i]-ths;
			    n[i]-=ths;
		//		ths=n;
				if(n[i]>100) {
					hds=n[i]/100;
					hds*=100;
					hds=n[i]-hds;
				   n[i]-=hds;
		//			hds=n;
					if(n[i]>1000) {
						tns=n[i]/1000;
						tns*=1000;
						tns=n[i]-tns;
						n[i]-=tns;
		//				tns=n;
					}
				}
			}
				int count=1;
			
			if(ths!=0) {
				count++;
				if(hds!=0) {
					count++;
					if(tns!=0) {
						count++;
					}
				}
			}
			System.out.println(count);
			
			
			System.out.print((hds!=0?hds+" ":""));
			System.out.print((ths!=0?ths+" ":""));
			
			System.out.print((tns!=0?tns+" ":""));
			System.out.println(n[i]);
			
		
		} */
		

	}

}