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 main():
  from sys import stdin, stdout
  n = stdin.readline()
  n = int(n)
  # k = int(k)
  # print(n)
  # cnt = 0
  res = 0
  lines = stdin.readlines()
  for line in lines:        
    a = line
    leng = len(a) - 2
    # print(a, leng)
    res = []
    for n in a:
      if n == '\n':
        break
      # print(n)
      if int(n) != 0:
        res.append(int(n)*10**leng)
      leng -= 1
    print(len(res))
    for i in res:
      stdout.write(str(i) + ' ')
    stdout.write('\n')
  # stdout.write(res)
  
if __name__ == "__main__":
  main()