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,y = map(int,input().split())
#arr = [int(i) for i in input().split()]
from collections import Counter
import math
mod = 10**9+7
 
for i in range(int(input())):
	n = int(input())
	#n,k = map(int,input().split())
	#arr = [int(i) for i in input().split()]
	ans = []
	# while(n>0):
	# 	x = len(n)
	# 	ans.append(10**x)
	# 	n -= 10**x
	x = str(n)
	c = 0
#	n = str(n)
#	print(len(x))
	a = []
	for i in range(len(x)):
		y = int(x[len(x)-i-1]) * 10**i
#		print(y)
		ans.append(y)
	for i in ans:
		if i!=0:
			a.append(i)
			c += 1
			#print(i)
		#ans.append(x[len(x)-i-1] * 10**i)
	print(c)
	print(*a)