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:
n =int(input())
l = []
k = []
for i in range(n):
   o = 0
   p = int(input())
   if str(p)[-1]==0:
      l.append(1)
      k.append(p)
   else:
      j = str(p)[::-1]
      for q in range(len(j)):
         if j[q]!= '0':
            c = ''
            c = j[q] + '0'*q
            k.append(int(c))
            o += 1
      l.append(o)
for i in range(n):
   print(l[i])
   for j in range(l[i]):
      print(k[0], end=" ")
      k.remove(k[0])
   print()