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:
digit = 0
nbSum = 1
nbMult = 0
flag = 0
array = []


def init():
    global digit, nbSum, nbMult, flag, array
    digit = 0
    nbSum = 1
    nbMult = 0
    flag = 0
    array = []
    return


def execution(x):
    global digit, nbSum, flag
    if x % 10 != 0:
        nbSum += 1
        flag = 1
        while x % 10 != 0:
            x -= 1
            digit += 1
        array.append(digit)
    else:
        flag = 0
    return


def resolveProblem():
    global digit, nbSum, nbMult, flag
    t = int(input())

    while t // 10 > 0:
        execution(t)
        digit = 0
        t = t // 10
        if nbMult > 0 and flag == 1:
            array[-1] = array[-1] * (10 ** nbMult)
            flag = 0
        nbMult += 1

    array.append(t * (10 ** nbMult))
    return


if __name__ == '__main__':
    n = int(input())
    for i in range(n):
        init()
        resolveProblem()
        print(nbSum)
        for j in range(nbSum):
            if j == nbSum - 1:
                print(array[j])
            else:
                print(array[j], end=' ')