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:
import sys
import math

def is_round(a):
    if 1 <= a <= 9:
        return True
    else:
        s = list(int(i) for i in str(a)[1:])
        if sum(s) == 0:
            return True
        else:
            return False


t = int(sys.stdin.readline().split()[0])

numbers = []

for line in sys.stdin:
    for word in line.split():
        numbers.append(int(word))


for number in numbers:
    if is_round(number):
        print(1)
        print(number)
    else:
        power = int(math.log10(number))

        i = power
        k = 0
        s = ""

        while i >= 0:
            digit = int(str(number)[power - i])
            if digit == 0:
                i -= 1
                continue
            else:
                t = pow(10, i) * digit
                s += str(t) + " "
            k += 1
            i -= 1
        print(k)
        print(s)