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:
#lannisters don't act like fools


'''And who are you, the proud lord said,
That I must bow so low?
Only a cat of a different coat,
That's all the truth I know.
In a coat of gold or a coat of red,
A lion still has claws,
And mine are long and sharp, my lord,
As long and sharp as yours.
And so he spoke, and so he spoke,
That lord of Castamere,
But now the rains weep o'er his hall,
With no one there to hear.
Yes now the rains weep o'er his hall,
And not a soul to hear.
'''


import math
t=int(input())
for _ in range(0,t):
    n=input()
    lst=[]
    for i in range(len(n)-1,-1,-1):
        if n[i]!='0':
            lst.append(n[i]+'0'*(len(n)-1-i))
    print(len(lst))
    for i in range(0,len(lst)):
        print(lst[i],end=' ')
    print()