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 solve(tests):
    def helper(num):
        result = [1]
        if num <= 0:
            return [0]
        elif num < 10:
            result[0] = 1
            result.append(num)
            return result
        else:
            nextResult = helper(int(str(num)[1:]))
            totalLen = len(str(num))
            firstDigit = int(str(num)[0])
            return [nextResult[0] + 1] + [firstDigit * 10 ** (totalLen - 1)] + nextResult[1:]
    
    for test in tests:
        ans = helper(test)
        print(ans[0])
        print(*ans[1:])

t = int(input())
tests = []
for _ in range(t):
    tests.append(int(input()))
solve(tests)