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 countDigit(n): 
    count = 0
    while n != 0: 
        n //= 10
        count+= 1
    return count 
 
def zero_checker(n):
    c=0
    while n:
        rem=n%10
        if rem==0:
            c=c+1
        n=n//10
    return c 
    

test=int(input())
for i in range(test):
    min_nums=0
    n=int(input())
    num_digits=countDigit(n)
    if num_digits==1:
        min_nums=1
        print(min_nums)
        print(n)
    else:
        if n%(10**(num_digits-1))==0:
            min_nums=1
            print(min_nums)
            print(n)
        else:
            chk=zero_checker(n)
            min_nums=num_digits-chk
            print(min_nums)
            i=0
            while n!=0:
                rem=n%10
                if rem!=0:
                    print(rem*(10**i),end=" ")
                n=n//10
                i=i+1