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:
#round


INPUT=True

def func(ip):
	num=ip
	temp_ls=[]
	res_ls=[]
	
	#temp_ls=list(str(num))
	#temp_ls=map(int, temp_ls)
	for i in str(num):
		temp_ls.append(int(i))
	#return(temp_ls)
	
	for i in range(len(temp_ls)):
		if i == 0 and temp_ls[i] != 0:
			temp = True
			res_ls.append(temp_ls[i]*(10**(len(temp_ls)-1)))
		elif temp and temp_ls[i] != 0:
			res_ls.append(temp_ls[i]*(10**(len(temp_ls)-i-1)))
		
	temp=False
	
	return(res_ls)
	




func_ls=[]

while INPUT:
	t=input()
	for i in range(int(t)):
		ip=input()
		ip=int(ip)
		if ip <= 10**4 and ip >=1:
			func_ls.append(func(ip))
			#func_ls=map(int, func_ls)
		
	for i in range(len(func_ls)):
		t_ls=[]
		#for j in func_ls[i]:
		print(len(func_ls[i]))
		t_ls=map(str,func_ls[i])
		print(' '.join(t_ls))
	#print(func_ls)
	INPUT=False