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 is_round(s):
    cnt = 0
    li = ['0','00','000','0000']
    if s[0].isnumeric() and s[1:] in li:
        return 1
    else:
        return 0
def find_sum(s):
    li = []
    new_li = []
    zero = ['0','00','000','0000']
    if is_round(s) == 1:
        new_li.append(s)
    else:
        s = list(s)
        for i in range(len(s)):
            li.append(s[i]+'0'*(len(s)-i-1))
        for i in range(len(li)):
            if li[i] not in zero:
                new_li.append(li[i])
    return len(new_li), new_li

for _ in range(int(input())):
    n = input()
    x, li = find_sum(n)
    print(x)
    print(' '.join(li))