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 PYTHON):

Solution:
dict1={'4':'10000','3':'1000','2':'100','1':'10','0':'1'}
n=int(input())
lst=[]
for i in range(0,n):
    lst.append(str(input()))
l=len(lst)
r=0
while l!=0:

    q=lst[r]
    lst1=[]
    lst2=[]
    for i in range(0,len(q)):
        lst1.append(int(q[i]))
    # print lst1
    r=r+1
    p=len(lst1)
    i=0
    while p!=0:
        if lst1[i]!=0:
          x=p-1
          lst2.append(lst1[i]*int(dict1[str(x)]))
        else:
            pass

        i=i+1
        p=p-1
    print len(lst2)
    c=' '.join(map(str,lst2))
    print c
    l=l-1