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 final class Main
{
public static void main(String[] args)
{
Scanner sc=new Scanner(System.in);
int k=sc.nextInt();
int temp[]=new int[k];
for(int j=0;j<k;j++)
temp[j]=sc.nextInt();

for(int j=0;j<temp.length;j++)
{
int n=temp[j];
int len=(n+"").length();
String sn=n+"";
int a[]=new int[len];
String res="";
for(int i=0;i<len-1;i++)
{
    int temp1=(Integer.parseInt(sn.charAt(i)+"")*(int)Math.pow(10,(len-i-1)));
    if(temp1>0)
    res+=temp1+" ";
}
if(sn.charAt(sn.length()-1)!='0')
res+=sn.charAt(sn.length()-1);
System.out.println(res.trim().split(" ").length);
System.out.println(res.trim());
}
}

}