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:
def sum_round(x):
    x = list(map(int, str(x)))
    len_str = len(x)

    list_tmp = []
    for idx, i in enumerate(x):
        if idx != len_str:
            if i == 0:
                continue
            tmp = ['0' for x in range((len_str - (idx + 1)))]
            res = [str(i)] + tmp
            
            res = ''.join(res)
            list_tmp.append(res)
        if idx == (len_str - 2):
            res = str(i)
    return list_tmp


a = int(input())
while a != 0:
    x = int(input())
    if x < 10:
        print(1)
        print(x)
        a -= 1
    elif (x % 10 == 0) & (x < 101):
        print(1)
        print(x)
        a -= 1
    else:
        x = sum_round(x)
        x = list(map(int, x))
        print(int(len(x)))
        print(*x)         
        a -= 1