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 math


def get_num(): return list(map(int, input().rstrip().split()))


def rotate(my_list, num): return my_list[num:] + my_list[:num]


def main():
    num = int(input())

    for i in range(num):
        mynum = input()
        array = len(mynum) * [0]
        mynum = int(mynum)
        cont = 0
        scaler = 1
        while (mynum >= 1):
            digit = math.floor(mynum % 10)
            array[cont] = digit * scaler
            cont += 1
            scaler *= 10
            mynum /= 10

        if 0 in array:
            array = list(set(array))
            array.remove(0)
            print(len(array))
            print(' '.join(map(str, array)))
        else:
            print(len(array))
            print(' '.join(map(str, array)))

main()

list = [1,2,3,4]