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:
def ans(t):
	l1=[]
	l2=[]
	for i in range(int(t)):
		l1.append(input())
	for en in l1:
		size=len(en)
		c=0
		while(int(en)>0):
			tp=(int(en)%10)*(10**c)
			c+=1
			l2.append(tp)
			en = int(int(en)/10)

		s=''
		#for i in l2:
		#	if str(i) == '0':
		#		l2.remove(i)
		for j in range(len(l2)-1):
			if 0 in l2:
				l2.remove(0)
		print(len(l2))
		for i in l2:
			s+=' '+str(i)

		print(s[1:])
		l2 = []
	return

t=input()
ans(t)