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 createList(a_string):
	a_string = list(a_string)
	a = []
	for i in a_string:
		a.append(int(i))
	return a

def simpleSlag(a_list):
	b = len(a_list)-1
	flag = 0
	ans = []
	c = 10**b
	for i in a_list:
		if i!=0:
			flag+=1
			ans.append(i*c)
		else:
			pass
		c= int(c/10)
	return flag,ans

def outputResults(resSlag):
	print(resSlag[0], end="\n")
	b = resSlag[1]
	for i in b:
		print(i,end = " ")
	print(end="\n")

def inputResults():
	t = int(input(""))
	resSlags = []
	for i in range(t):
		j = createList(input(""))
		resSlags.append(simpleSlag(j))
	for i in range(len(resSlags)):
		outputResults(resSlags[i])

inputResults()