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:
n = int(input())
inp = []
ret = []

def int_len(ch):
    return(len(str(ch)))

for i in range(n):
    new = int(input())
    inp.append(new)
    new_arr = list(map(int, str(new)))
    while len(new_arr) > 0:
        a = new_arr[0]
        if a == 0:
            del(new_arr[0])
        else:
            if len(ret) < i+1:
                ret.append([])
            ret[i].append(str(a*(10**(len(new_arr)-1))))
            del(new_arr[0])

for i in range(len(ret)):
    print(len(ret[i]))
    print(' '.join(ret[i]))