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 solution(n:int):
  arr=[]
  i=0
  copy_n=n
  k=n
  len_1=0
  while(copy_n!=0):
    copy_n//=10
    len_1+=1
  mul=0
  while(i<len_1):
    if(n%10!=0):
      arr.append((n%10)*(10**mul))
    n//=10
    mul+=1
    i+=1
  return arr
t=int(input())
a=[]
ans=[]
ans_1=[]
for i in range(t):
  c=int(input())
  a.append(c)
  ans.append(solution(a[i]))
for i in range(len(a)):
  print(len(ans[i]))
  print(*ans[i])