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:
t = int(input())
lis = []
for i in range(t):
   b = input()
   lis.append(int(b))

for i in lis:
   digits = str(i)
   num = len(digits)

   if num == 1 or digits[1:]=='0'*(num-1):
      print('1')
      print(digits)	
   else:
      c = 0
      l = []
      for k in range(num):
         if digits[k]!='0':
            c+=1
            if num-k-1 == 0:
               l.append(str(digits[k]))
            else :
               l.append(str(digits[k])+'0'*(num-k-1))
      print(c)
      for j in l:
         if str(j[0]) not in digits:
            continue
         print(j, end=' ')

      print('')