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 isround(b):
	if b<10:
		return True
	elif list(str(b)).count(0) == (len(str(b))-1):
		return True
	else:
		return False		
n = int(input())
l = []   
for _ in range(n):		
	c = []
	a = int(input())
	if isround(a):
		c.append(a)
	else:
		b = list(str(a))
		b.reverse()
		for i in range(len(b)):
		    if b[i]!='0':
			    b[i] = int(b[i])*(10**i)
			    c.append(b[i])  	

	l.append(c)
	
for i in l:
	print(len(i))
	for j in i:
	    print(j,end=" ")