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 PYTHON):

Solution:
t=input()
j=0
while(j<t):
	j+=1
	a=input()
	if(a<=10):
		print(1)
		print(a)
	else:
		b=str(a)
		i=1
		d=[]
		d.append(int(b[0]))
		while(i<len(b)):
			if(b[i]=='0'):
				d=[10*x for x in d]
			else:
				d=[10*x for x in d]
				d.append(int(b[i]))
			i+=1
		print(len(d))
		k=0
		while(k<len(d)):
			if(k==len(d)-1):
				print(d[k])
			else:
				print(d[k]),
			k+=1