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())
t = [int(input()) for _ in range(n)]

# print(n, t)
for titem in t:
    sum = 0
    klist = []
    # 10 ^ 4
    for i in range(4, -1, -1):
        if titem // (10 ** i):
            sum += 1
            klist.append(titem // (10 ** i) * (10 ** i))
            titem = titem % (10 ** i)
    if sum > 0:
        if titem > 0:
            sum += 1
        print(sum)

    loop = 0
    for k in klist:
        if loop > 0:
            print(" ", end="")
        print(k, end="")
        loop += 1
    if titem > 0:
        print(titem)
    else:
        print("")