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:
x = input()
x = int(x)
u = []
def code(r):
  l = len(r)
  o = []
  k = 1
  o.append(int(r[0])*(10**(len(r)-1)))
  while k < l:
    if r[k] != "0":
      o.append(int(r[k])*(10**(len(r)-k-1)))
    
    k+=1
  print(len(o))
  b = 0
  while b < len(o):
    print(o[b], end = " ")
    b+=1
  print("")

z = 0
while z < x:
  y = input()
  u.append(y)
  z+=1
f = 0


while f < x:
  code(u[f])
  f+=1