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:
t = int(input())

num_list = []

count = 0

while count < t :
    n = int(input())
    num_list.append(n)
    count +=1

for x in num_list :
    num_s = 0
    sum_num = []
    if len(list(str(x))) == 1 :
        num_s += 1
        print (num_s)
        print (x)
    else:
        rem = x%10
        if rem != 0 :
            sum_num.append(str(rem))
            x = x - rem
        num_zeros = len(list(str(x))) - 1
        x = x//10
        for y in list(str(x)):
            n = str(int(y)*(10**num_zeros))
            if n != "0":
                sum_num.append(n)
                num_zeros -= 1
            else:
                num_zeros -=1
        print (len(sum_num))
        print (" ".join(sum_num))