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 next(n):
	arr = []
	n = str(n)
	l = len(n)
	for i in range(l):
		if int(n[i]) != 0:
			arr.append(n[i] + '0'*(l-i-1))

	print(len(arr))
	for i in arr:
		print(i,end = ' ')
	print()
	return 


    
n = int(input())

#for t in range(int(input())):
'''a,b = map(int,input().split())
arr = list(map(int,input().split()))
qarr = []
for i in range(b):
	qarr.append(int(input()))

#k = input()
#n = int(input())
Sol(a,b,arr,qarr)'''
for i in range(n):
	next(int(input()))