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:
N = int(input())
answers = []
for i in range(N):
    x = int(input())
    done = False
    if x < 10:
        done = True
        answers.append({1: [x]})
    elif str(x).count("0") + 1 == len(str(x)):
        done = True
        answers.append({1: [x]})

    if not done:
        numbers = []
        cnt = 0
        reductor = pow(10, len(str(x)) - 1)
        for num in str(x):
            if num != "0":
                cnt += 1
                numbers.append(int(num) * reductor)
            reductor = reductor // 10
        answers.append({cnt: numbers})

for i in answers:
    print(list(i.keys())[0])
    for k in i[list(i.keys())[0]]:
        print(k, end=" ")
    print()