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():
    test_cases = int(input())
    round_nums = [10000]
    for num in range(1, 10):
        num = str(num)
        for i in range(4):
            new_num = num + ('0' * i)
            round_nums.append(int(new_num))
    round_nums.sort()
    for _ in range(test_cases):
        target_num = int(input())
        count = 0
        result = []
        while target_num > 0:
            flag = True
            i = 0
            while i < len(round_nums) and flag:
                if round_nums[i] >= target_num:
                    count += 1
                    if target_num == round_nums[i]:
                        target_num -= round_nums[i]
                        result.append(str(round_nums[i]))
                    else:
                        target_num -= round_nums[i-1]
                        result.append(str(round_nums[i-1]))
                    flag = False
                i += 1
        print(count)
        print(" ".join(result))

main()