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:
# your code goes here
n=int(input())
l=[]
for i in range(n):
	l.append(input())
for i in l:
	if int(i)<10:
		print(1)
		print(i)
	else:
		a=len(str(i))
		l2=[]
		cnt=0
		j=i
		while a>0:
			n1=pow(10,a-1)
			if int(j)%n1==0:
				cnt+=1
				l2.append(j)
				break
			else:
				m=int(j)%n1
				n=int(j)-m
				l2.append(n)
				cnt+=1
				j=m
				if j>0:
					a=len(str(j))
				else:
					a=0
		print(cnt)
		print(*l2)