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 PYTHON):

Solution:
def round():
    i = input()
    flag = True
    result = []
    res = []

    while i > 0:
        n = int(raw_input())
        while flag:
            to_get_first_num = int('1' + '0' * (len(str(n)) - 1))
            first_num = str(n / to_get_first_num)
            divide_with = int(first_num + '0' * (len(str(n)) - 1))
            q, r = divmod(n, divide_with)
            res.append(divide_with)
            n = r

            if r == 0:
                flag = False

        result.append(res)
        res = []
        flag = True
        i -= 1

    for i in result:
        print len(i)
        for j in i:
            print j,
        print ''


round()