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):
	t=int(input())
	if t<10:
		li=[t]
		print(len(li))
		print(t)
	elif t<100:
		if t%10==0:
			print(1)
			print(t)
		else:
			A=t%10
			B=t%100-A
			li=[B,A]
			print(len(li))
			print(B,A)
	elif t<1000:
		A=t%10
		B=(t%100-A)
		C=(t%1000-A-B)
		if t%100==0:
			print(1)
			print(t)
		elif t%10==0:
			print(2)
			print(C,B)
		elif (t-A)%100==0:
			print(2)
			print(C,A)
		else:
			li=[A,B,C]
			print(len(li))
			print(C,B,A)
	elif t<=10000:
		A=t%10
		B=(t%100-A)
		C=(t%1000-A-B)
		D=(t%10000-A-B-C)
		if t==10000:
			print(1)
			print(t)
		elif t%1000==0:
			print(1)
			print(t)
		elif t%100==0:
			print(2)
			print(D,C)
		elif t%10==0:
			if (t-B)%1000==0:
				print(2)
				print(D,B)
			else:
				print(3)
				print(D,C,B)
		elif(t-A)%100==0:
			if (t-A)%1000==0:
				print(2)
				print(D,A)
			else:
				print(3)
				print(D,C,A)
		elif (t-B-A)%1000==0:
			print(3)
			print(D,B,A)
		else:
			li=(A,B,C,D)
			print(len(li))
			print(D,C,B,A)
	else:
		print("out")