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:
x=int(input(""))
m=0
list=[]
list1=[]
list2=[]
for c in range(x):
	y=input("")
	list.append(y)
	for i in range (len(list[c])):
		if int(list[c][i]) > 0 :
			m+=1
	list1.append(m)
	m=0
	for z in range (len(list[c])):
		number=1
		if len(list[c])==5:
				number=10000
		if len(list[c])==4 and z==0: 
				number=1000
		if len(list[c])==3 and z==0:
				number=100
		if len(list[c])==2 and z==0:
				number=10
		if len(list[c])==4 and z==1:
				number=100
		if len(list[c])==3 and z==1:
				number=10							
		if len(list[c])==4 and z==2:
				number=10		
		if int(list[c][z]) > 0:
			list2.append((int(list[c][z]))*number) 
n=0			
for j in range(len(list1)):
	print(list1[j])	
	if list1[j]==1:				
		print(str(list2[n]))
		n+=1
	if list1[j]==2:
		print(list2[n],list2[n+1])
		n+=2
	if list1[j]==3:
		print(list2[n],list2[n+1],list2[n+2])
		n+=3
	if list1[j]==4:
		print(list2[n],list2[n+1],list2[n+2],list2[n+3])		
		n+=4