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:
''' SUm of Round NUmbers
'''

import bisect as bi

MAX = 10**4+1
roundd = []
roundd_set = set()
def precompute():
    for i in range(1, MAX):
        if str(i).count('0') == len(str(i)) - 1:
            roundd.append(i)

    roundd_set = set(roundd)
    # print(roundd_set)
    return roundd_set


def search(val):
    lo, hi = 0, len(roundd)-1
    while lo < hi:
        mid = lo + (hi - lo)//2
        print(mid)
        if roundd[mid] > val:
            hi = mid
        else:
            lo = mid+1

    return lo


def solve(n):
    if n in roundd_set:
        return 1, [n]

    num = n
    c = 1
    res = []
    while num not in roundd_set:
        idx = bi.bisect_left(roundd, num)
        # print(num - roundd[idx-1])
        res.append(roundd[idx-1])
        num -= roundd[idx-1]
        # print(num in roundd)
        # break
        c += 1

    res.append(num)
    return c, res


roundd_set = precompute()
for _ in range(int(input())):
    n = int(input())

    result = solve(n)
    print(result[0])
    print(*result[1])