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:
def is_round(x):
    n=len(x)
    num="1"+("0"*(n-1))
    num=int(num)
    x_2=int(x)
    if x_2 %num==0:
        return True
    else:
        return False
    
    
def modulo(n):
    
    n=str(n)
    i=0
    res=""
    while i<len(n):
        if n[i]!='0':
            res+=str(int(n[i])*(10**(len(n)-i-1)))+" "
        i+=1
    return res
        
    


t=int(raw_input())

i=0



while i<t:
    input=int(raw_input())
    if is_round(str(input)):
        print(1)
        print(input)
    else:
        
        res=modulo(input)
        print(len(res[:len(res)-1].split(" ")))
        print(res[:len(res)-1])
    i+=1