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:
num_test_case = int(input())
list_output = []
min_no_sum = []
while num_test_case > 0:
    num = int(input())
    temp = num
    count = 0
    while temp > 0:
        temp = int(temp / 10)
        count += 1
    temp = num
    sum_count = 0

    while temp > 0 and count > 0:
        quetient = int(temp / (10 ** (count - 1)))
        if quetient > 0:
            list_output.append(int(quetient * (10 ** (count - 1))))
            sum_count += 1
            temp = int(temp % (10 ** (count - 1)))
        count -= 1
    min_no_sum.append(sum_count)
    num_test_case -= 1

i = 0
while i < len(list_output):
    for j in min_no_sum:
        print(j)
        while j > 0:
            print(list_output[i], end=" ")
            i += 1
            j -= 1
        print()