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 main():
    cases = input()
    for i in range(int(cases)):
        curr = int(input())
        if (curr > 0):
            places = [False, False, False, False]
            s = str(curr)
            count = 0
            a = len(s) - 1
            while (a >= 0):
                if (s[a] != '0'):
                    places[a] = True
                    count += 1
                a -= 1
            if (count <= 1):
                print(1)
                print(s)
            else:
                print(count)
                a = len(s) - 1
                toprint = ""
                while (a >= 0):
                    if (places[a]):
                        digit = int(s[a])
                        if (digit != 0):
                            toprint += str(digit * (10 ** (len(s) - a - 1))) + " "
                    a -= 1
                print(toprint)
main()