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:
import sys 
from collections import defaultdict
import random
import math

def chk(s):
	for i in s:
		if i!='0':
			return 0
	return 1

def round(s):
	if len(s)==1:
		return 1

	if s[0]!='0' and chk(s[1:])==1:
		return 1
	return 0

t = int(input())

for _ in range(t):

	s = input()
	n = int(s)

	if round(s):
		print(1)
		print(s)
		continue


	l = len(s)
	v = []
	for i in range(l):
		if s[i]!='0':
			x = s[i]+'0'*(l-i-1)
			v.append(x)
	print(len(v))

	for i in v:
		print(i,end= ' ')
	print()