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:
def main():
    t = int(input ())
    # t is the number of test cases
    for i in range (t): 
        case = int(input ())
        # case is the test value given
        answer = " "
        addends = 0
        # addends is the final number of minimum addends required
        for digit in range (len(str(case))):
            # to take each digit in the test value and obtain face valu, place value and total min. addends
            face_value = (case // 10**digit) % 10
            if face_value != 0:
                place_value = face_value * (10** digit)
                answer =  str(place_value) + " " +answer
                addends += 1 
        print (addends)
        print (answer)
            
main ()