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:
# Codeforces 640 D4
# Sum of Round Numbers

import sys

def solve():
	return None

def main():
	q = []
	for line in sys.stdin.readlines():
		q.append(line)

	for i in range(len(q)):
		q[i] = q[i].rstrip().split(' ')[0]

	for i in range(1, len(q)):
		num = q[i]
		nums = []
		count = 0
		zeros = ""
		for j in range(len(q[i])-1, -1, -1):
			if q[i][j] != '0':
				zeros += ("0" * count)
				nums.append (str(q[i][j]) + zeros)
			count+=1
			zeros = ""
		print(len(nums))
		print(*nums)
		# start = 1;
		# d = len(str(q[i]))
		# nums = []
		# for i in range(d):
		# 	nums.append()

if __name__ == '__main__':
	main()