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:
for i1 in range(int(input())):
	n=input()
	if len(n)==1:
		print(1)
		print(n)
		continue
		
	else:
	
		a=n[0]
		b=n[1:]
		if b=="0" * (len(n)-1):
			print(1)
			print (n)
		else:
			x=int(n)
			c=0
			zero=1
			l1=[]
			while x!=0:
				y=x%10
				if y!=0:
					c+=1
					
					l1.append(y*pow(10,zero-1))
					#print (x%10)
				zero+=1
				x=x//10
			print(c)
			for i in l1:
				print(i,end=' ')
			print()