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:
n=int(input())
for i in range(n):
	a=input()
	x=len(a)
	if int(a)<11 or x-1==a[1:].count('0'):
		print(1)
		print(a)
	else:
		a=int(a)
		t=a
		q=[]
		for i in range(x):
			if a%10!=0:
				r=a%10
				q.append(r*(10**i))
				a=a//10
			else:
				a=a//10
		s=t-sum(q)
		if s>0:
			print(s,end=' ')
			t=1
		else:
			t=0
		print(len(q)+t)
		print(*q)