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 isround(n):
  n = str(n)
  if len(n)==1: return True
  n = n[1:]
  if int(n) == 0: return True
  return False 

def solve(ls):
  for n in ls:
    temp=[]
    i=1
    for _ in range(len(str(n))):
      if isround(n): temp.append(n); break
      if n%(10**i)!=0: temp.append(n%(10**i))
      n=(10**i)*(n//10**i)
      i+=1
    print(len(temp))
    for i in temp: print(i,end=' ')
    print()
if __name__ == '__main__':
  t = int(input())
  #ls = [5009,7,9876,10100,10,0,909090010]
  ls = []
  for i in range(t): ls.append(int(input()))
  solve(ls)