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 gen_all_beatiful():
	res = []
	for i in range(1, 10):
		cur = i 
		for j in range(5):
			if cur > 10000:
				break
			res.append(cur)
			cur *= 10
	res.sort(reverse=True)
	return res



def main():
	all_beatiful = gen_all_beatiful()

	numbers = int(input())
	for i in range(numbers):
		num = int(input())
		res = []
		for elem in all_beatiful:
			if num == 0:
				break
			if num >= elem:
				res.append(elem)
				num -= elem
		print(len(res))
		print(*res)


if __name__ == '__main__':
	main()