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:
items = int(input())
numbers = []

for i in range(items):
    numbers.append(int(input()))


def check(num):
    answer = []
    if len(str(num)) == 1:
        answer.append(num)
    elif len(str(num)) == 2:
        if num % 10 == 0:
            answer.append(num)
        else:
            answer.append(num // 10 * 10)
            answer.append(num % 10)

    elif len(str(num)) == 3:
        answer.append(num // 100 % 10 * 100)
        if num % 100 // 10 != 0:
            answer.append(num % 100 // 10 * 10)
        if num % 10 != 0:
            answer.append(num % 10)

    elif len(str(num)) == 4:
        answer.append(num // 1000 * 1000)
        if num // 100 % 10 != 0:
            answer.append(num // 100 % 10 * 100)
        if num % 100 // 10 != 0:
            answer.append(num % 100 // 10 * 10)
        if num % 10 != 0:
            answer.append(num % 10)
    else:
        answer.append(num)
    print(len(answer))
    for i in answer:
        print(i, end=' ')
    print()


for num in numbers:
    check(num)