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 find_round_numbers(number):
    round_numbers_array = []
    numberOfDigits = len(str(number)) - 1
    while number != 0:
        round_numbers_array.append(int(number % 10))
        number = int(number / 10)
    round_numbers_array.reverse()
    round_numbers_array_with_tens = []
    for i in round_numbers_array:
        if i != 0:
            round_numbers_array_with_tens.append(i * pow(10, numberOfDigits))
        numberOfDigits -= 1
    return round_numbers_array_with_tens


number_of_test_cases = int(input())
while number_of_test_cases != 0:
    number = int(input())
    round_number_array = find_round_numbers(number)
    print(len(round_number_array))
    print(" ".join(map(str, round_number_array)))
    number_of_test_cases -= 1