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  integer(array):
    for i in range(len(array)):
        array[i] = int(array[i])
    return array


N = int(input())
inputs = []
for i in range(N):
    inputs.append(integer(str(input()).split(' ')))


def split(word): 
    return [char for char in word]

def arraystring(array):
    string = ""
    for i in range(len(array) - 1):
        string += str(array[i])
        string += " "
    string += str(array[len(array) - 1])
    return string

def round(n):
    sum = 0
    rounding = []
    d = integer(split(str(n)))
    for i in range(len(d)):
        if(d[i] != 0):
            sum += 1
            rounding.append(d[i] * (10 ** (len(d) - i - 1)))
    return [sum, arraystring(rounding)]

for i in inputs:
    print(round(i[0])[0])
    print(round(i[0])[1])