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 PYTHON):

Solution:
from __future__ import division
from __future__ import print_function


import itertools

input = raw_input
range = xrange

filter = itertools.ifilter
map = itertools.imap
zip = itertools.izip


def read_int():
    return int(input())


def read_ints():
    return list(map(int, input().split(' ')))


def read_str():
    return input()


def read_strs():
    return input().split(' ')


def solve():
    n = read_int()

    cnt = 0
    mult = 1
    summands = []
    while n > 0:
        d = n % 10
        if d != 0:
            summands.append(d * mult)
            cnt += 1

        mult *= 10
        n //= 10

    print(cnt)
    for a in summands:
        print(a, end=" ")
    print()


t = read_int()
for case in range(t):
    solve()