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 class HelloWorld{
    void solve(){
        Scanner S = new Scanner( System.in ) ;
        int n = S.nextInt() ;
        // int n = 5 ;
        int[] arr = new int[ n ] ;
        for( int i=0;i<n;++i ) arr[i] = S.nextInt();
        // int arr[] = { 5009 , 7 , 9876 , 10000 , 10 } ; 
        int len = 0 ;
        for( int i:arr ) {
            if( i<10 ){ 
                System.out.println( "1" ) ;
                System.out.println( i ) ;
            }
            else {
                String str  = Integer.toString( i ) ;
                StringBuilder sb = new StringBuilder() ;
                sb.append( str ) ;
                sb.reverse() ;
                str = sb.toString() ;
                List<String> list = new ArrayList<>() ;
                int check = 0 ;
                for( int j=str.length()-1;j>=0;j-- ) {
                    if( str.charAt(j)=='0' ) {
                        check++ ;
                        continue ;
                        
                    }
                    String result = "" ;
                    int curr = j ;
                    while( curr!=0 ) {
                        curr-- ;
                        result += '0' ;
                    }
                    result = str.charAt(j)+result ;
                    list.add( result ) ;
                }
                if( str.length()-1==check ){
                    System.out.println( 1 ) ;
                    System.out.println( sb.reverse() ) ;
                }else {
                    System.out.println( list.size() ) ;
                    while( !list.isEmpty() ) {
                        System.out.print( list.get(0)+" " ) ;
                        list.remove( 0 ) ;
                    }
                    System.out.println() ;
                }
            }
        }
    }
    public static void main(String []args){
        HelloWorld obj = new HelloWorld() ;
        obj.solve() ;
    }
}