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:
t = int(input())
for _ in range(t):
    num = int(input())
    res,power = [],1
    while num > 0:
        if num%10 > 0:
            temp = (num%10)*power
            res.append(temp)
        num = num // 10
        power *=10
    res = [int(i) for i in res]
    print(len(res))
    print(*res)
# testcase = int(input())
# for _ in range(testcase):
#     num = int(input())
#     l = list(str(num))
#     l = [int(i) for i in l]
#     count,res = 0,[]
#     l = l[::-1]
#     for i,n in enumerate(l[:-1]):
#         if n != 0 :
#             count += 1
#             res.append(n*pow(10,i))
#     count += 1
#     res.append(l[-1]*pow(10,len(l)-1))
#     print(count)
#     print(*res)