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():
    num_test_cases = int(input())
    output = ""
    
    for i in range(0, num_test_cases):
        test_case_str = input()
        test_case = int(test_case_str)
        if test_case < 10:
            output += f"1\n{test_case}\n"
            continue
        digits = len("%i" % test_case)
        number_of_sums = 0
        parts = []
        for t in range(0, digits):
            summand = int(test_case_str[t]) * pow(10, len("%i" % test_case)-1)
            if summand != 0:
                parts.append(summand)
                number_of_sums+=1
                test_case -= summand
        output += str(len(parts)) + "\n" + " ".join(str(n) for n in parts) + "\n"
    print(output)

if __name__ == "__main__":
    main()