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())

def is_ok(k: int) -> bool:
    while k != 0:
        if k % 10 != 0 and k > 9:
            return False
        k = k // 10

    return True


# for i in range(1, 10):
#     assert is_ok(i)

# assert is_ok(10)
# assert is_ok(4000)
# assert is_ok(700)
# assert is_ok(70)
#
# assert not is_ok(110)
# assert not is_ok(110)
# assert not is_ok(707)
# assert not is_ok(202)
# assert not is_ok(222)
# assert not is_ok(1001)

def find_max_ok(n: int) -> int:
    first = n
    total_digist = 1
    while first > 9:
        first = first // 10
        total_digist += 1

    return first * 10**(total_digist-1)


def solve(n: int) -> list:
    ans = []

    while n != 0:
        m = find_max_ok(n)
        ans.append(m)
        n -= m

    return ans


for test in range(T):
    n = int(input())
    arr = solve(n)
    print(len(arr))
    for el in arr:
        print(el, end=" ")
    print()