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 PYTHON3):

Solution:
n=int(input())

for i in range(n):
    
    #get integer
    #integer=10
    integer=int(input())
    
    #length=2
    length=len(str(integer))

    #sinteger="10"
    sinteger=str(integer)

    #checking status
    summ=0
    

    #answer
    round_numbers=[]

    for i in range(len(sinteger)):
        
        summ=summ+int((sinteger[i]+("0"*(length-1-i))))
        
        round_numbers.append(int((sinteger[i]+("0"*(length-1-i)))))
        
        if(summ==integer):
            break
        
    round_numbers.sort()
    
    while(round_numbers[0]==0):
        round_numbers.pop(0)

    print(len(round_numbers))

    answer=""
    for y in range(len(round_numbers)):
        
        if(y==0):
            
            answer=str(round_numbers[y])
        else:
            
            answer=answer+" "+str(round_numbers[y])

    print(answer)