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 no_round(x):
    length = len(x)
    count = 0
    zeros = 0
    list_x = []
    for i in x:
#        print('', i, 'lenght', length, 'count', count, 'zeros', zeros)
        if i == '0':
            length = length - 1
            zeros = zeros + 1
            count = count + 1
            continue
        list_x.append(i + '0' * (length - 1))
        count = count + 1
        length = length - 1

    print(count - zeros)
    print(' '.join(list_x))
    return


import sys

def main():

  n_cases = None
  for line in sys.stdin:
      if not n_cases:
          n_cases = line
          continue
      line = line.strip()
      line = line.rstrip()
      no_round(line)

main()